Methods for determining whether an existing concrete composition is overdesigned

ABSTRACT

Design optimization methods can be used to design concrete mixtures having optimized properties, including desired strength and slump at minimal cost. The design optimization methods use a computer-implemented process that is able to design and virtually “test” millions of hypothetical concrete compositions using mathematical algorithms that interrelate a number of variables that affect strength, slump, cost and other desired features. The design optimization procedure utilizes a constant K (or K factor) within Feret&#39;s strength equation that varies (e.g., logarithmically) with concrete strength for any given set of raw material inputs and processing equipment. That means that the binding efficiency or effectiveness of hydraulic cement increases with increasing concentration so long as the concrete remains optimized. The knowledge of how the K factor varies with binding efficiency and strength is a powerful tool that can be applied in multiple circumstances. A concrete manufacturing process may include accurately measuring the raw materials to minimize variation between predicted and actual strength, as well as carefully controlling water content throughout the manufacturing and delivery process.

CROSS-REFERENCE TO RELATED APPLICATION

This application is a division of U.S. application Ser. No. 11/471,293,filed Jun. 19, 2006, which claims the benefit under 35 U.S.C. § 119(e)of U.S. Provisional Application Ser. No. 60/691,916, filed Jun. 17,2005. This application also claims the benefit of earlier filed andco-pending International Application No. PCT/US06/23863, filed Jun. 19,2006, which claims the benefit of U.S. Provisional Application Ser. No.60/691,916, filed Jun. 17, 2005. The disclosures of the foregoingapplications are incorporated herein in their entirety.

BACKGROUND OF THE INVENTION

1. The Field of the Invention

The invention is in the field of concrete compositions, moreparticularly in the design-optimization of concrete compositions basedon factors such as performance and cost. The invention more particularlyrelates to the design and manufacture of concrete using improved methodsthat more efficiently utilize all the components from a performance andcost standpoint and minimize strength variability, as well as uniquemethods for redesigning an existing concrete mix design and upgradingthe batching, mixing and/or delivery system of an existing concretemanufacturing plant.

2. The Relevant Technology

Concrete is a ubiquitous building material. Finished concrete resultsfrom the hardening of an initial cementitious mixture that typicallycomprises hydraulic cement, aggregate, water, and optional admixtures.The terms “concrete”. “concrete composition” and “concrete mixture”shall mean either the finished, hardened product or the initialunhardened cementitious mixture depending on the context. It may alsorefer to the “mix design”, which is the formula or recipe used tomanufacture a concrete composition. In a typical process formanufacturing transit mixed concrete, the concrete components are addedto and mixed in the drum of a standard concrete delivery truck,typically while the truck is in transit to the delivery site. Hydrauliccement reacts with water to form a binder that hardens over time to holdthe other components together.

Concrete can be designed to have varying strength, slump, and othermaterials characteristics, which gives it broad application for a widevariety of different uses. The raw materials used to manufacturehydraulic cement and concrete are relatively inexpensive and can befound virtually everywhere although the characteristics of the materialscan vary significantly. This allows concrete to be manufacturedthroughout the world close to where it is needed. The same attributesthat make concrete ubiquitous (i.e., low cost, ease of use, and wideavailability of raw materials) have also kept it from being fullycontrolled and its full potential developed and exploited.

Concrete manufacturing plants typically offer and sell a number ofdifferent standard concrete compositions that vary in terms of theirslump and strength. Each oz concrete composition is typicallymanufactured by following a standard mix design, or recipe, to yield acomposition that has the desired slump and that will harden intoconcrete having the desired strength. Unfortunately, there is often highvariability between the predicted (or design) strength of a given mixdesign and the actual strength between different batches, even in theabsence of substantial variability in the quality or characteristics ofthe raw material inputs. Part of this problem results from a fundamentaldisconnect between the requirements, controls and limitations of “field”operations in the concrete batch plant and the expertise from researchunder laboratory conditions. Whereas experts may be able to design aconcrete mixture having a predicted strength that closely reflectsactual strength when mixed, cured and tested, experts do not typicallyprepare concrete compositions at concrete plants for delivery tocustomers. Concrete personnel who batch, mix and deliver concrete to jobsites inherently lack the ability to control the typically largevariation in raw material inputs that is available when conductinglaboratory research. The superior knowledge of concrete by laboratoryexperts is therefore not readily applicable or transferable to theconcrete industry in general.

In general, concrete mixtures are designed based on such factors as (1)type and quality of hydraulic cement, (2) type and quality ofaggregates, (3) quality of water, and (4) climate (e.g., temperature,humidity, wind, and amount of sun, all of which can cause variability inslump, workability, and strength of concrete). To guarantee a specificminimum strength and slump as required by the customer (and avoidliability in the case of failure), concrete manufacturers typicallyfollow a process referred to as “overdesign” of the concrete they sell.For example, if the 28 day field strength of a particular concrete mixdesign is known to vary between 2500 psi and 4000 psi when manufacturedand delivered, a manufacturer must typically provide the customer with aconcrete composition based on a mix design that achieves a strength of4000 psi under controlled laboratory conditions to guarantee thecustomer a minimum strength of 2500 psi through the commercial process.Failure to deliver concrete having the minimum required strength canlead to structural problems, even failure, which, in turn, can leave aconcrete plant legally responsible for such problems or failure. Thus,overdesigning is self insurance against delivering concrete that is tooweak, with a cost to the manufacturer equal to the increased cost ofoverdesigned concrete. This cost must be absorbed by the owner, does notbenefit the customer, and, in a competitive supply market, cannot easilybe passed on to the customer.

Overdesigning typically involves adding excess hydraulic cement in anattempt to ensure a minimum acceptable strength of the final concreteproduct at the desired slump. Because hydraulic cement is typically themost expensive component of concrete (besides special admixtures used inrelatively low amounts), the practice of overdesigning concrete cansignificantly increase cost. However, adding more cement does notguarantee better concrete, as the cement paste binder is often a lowercompressive strength structural component compared to aggregates and thecomponent subject to the greatest dynamic variability. Overcementing canresult in short term microshrinkage and long term creep. Notwithstandingthe cost and potentially deleterious effects, it is current practice forconcrete manufacturers to simply overdesign by adding excess cement toeach concrete composition it sells than to try and redesign eachstandard mix design. That is because there is currently no reliable orsystematic way to optimize a manufacturer's pre-existing mix designsother than through time-consuming and expensive trial and error testingto make more efficient use of the hydraulic cement binder and/or accountfor variations in raw material inputs.

The cause of observed strength variability is not always wellunderstood, nor can it be reliably controlled using existing equipmentand following standard protocols at typical ready-mix manufacturingplants. Understanding the interrelationship and dynamic effects of thedifferent components within concrete is typically outside the capabilityof concrete manufacturing plant employees and concrete truck driversusing existing equipment and procedures. Moreover, what experts in thefield of concrete might know, or believe they know, about concretemanufacture, cannot readily be transferred into the minds and habits ofthose who actually work in the field (i.e., those who place concretemixtures into concrete delivery trucks, those who deliver the concreteto a job site, and those who place and finish the concrete at job sites)because of the tremendous difference in controls and scope of materialsvariation. The disconnect between what occurs in a laboratory and whatactually happens during concrete manufacture can produce flawed mixdesigns that, while apparently optimized when observed in thelaboratory, may not be optimized in reality when the mix design isscaled up to mass produce concrete over time.

Besides variability resulting from poor initial mix designs, anotherreason why concrete plants deliberately overdesign concrete is theinability to maintain consistency of manufacture. There are four majorsystemic causes or practices that have historically lead to substantialconcrete strength variability: (1) the use of materials that vary inquality and/or characteristics; (2) the use of inconsistent batchingprocedures; (3) overcementing; and (4) adding insufficient batch waterinitially and later making slump adjustments at the job site, typicallyby the concrete truck driver adding an uncontrolled amount of water tothe mixing drum. The total variation in materials and practices can bemeasured by standard deviation statistics.

The first cause of variability between theoretical and actual concretestrengths for a given mix design is variability in the supply of rawmaterials. For example, the particle size, size distribution,morphology, and particle packing density of the hydraulic cement andaggregates (e.g., course, medium, and fine) may vary from batch tobatch. Even slight differences can greatly affect how much water must beadded to yield a composition having the required slump. Because concretestrength is highly dependent on the water-to-cement ratio, varying thewater content to account for variations in the solid particlecharacteristics to maintain the required slump causes substantialvariability in concrete strength. Unless a manufacturer can eliminatevariations in raw material quality, overdesigning is generally the onlyavailable way to ensure that a concrete composition having the requiredslump also meets the minimum strength requirements.

Even if a concrete manufacturer accounts for variations in raw materialsquality, overdesigning is still necessary using standard mix designtables. Standardized tables are based on actual mix designs using onetype and morphology of aggregates that have been prepared and tested.They provide slump and strength values based on a wide variety ofvariables, such as concentration of cement, aggregates, water, and anyadmixtures, as well as the size of the aggregates. The use ofstandardized tables is fast and simple but can only approximate actualslump and strength even when variations in raw materials are measured.That is because the number of standardized mix designs is finite thoughthe variability in the type, quality and concentration (i.e., ratio) ofraw materials is virtually infinite. Because standardized tables canonly approximate real world raw material inputs, there can besignificant variability between predicted and actual strength when usingmix designs from standardized tables. Because of this variability, theonly two options are (1) time consuming and expensive trial and errortesting to find an optimal mix design for every new batch of rawmaterials or (2) overdesigning. Manufacturers typically opt foroverdesigning, especially in light of factors other than mix design thatcause variations between design and actual strength.

The second cause of strength variability is the inability to accuratelydeliver the components required to properly prepare each batch ofconcrete. Whereas modern scales can theoretically provide very accuratereadings, sometimes to within 0.05% of the true or actual weight,typical hoppers and other dispensing equipment used to dispense thecomponents into the mixing vessel (e.g., the drum of a concrete mixertruck) are often unable to consistently open and shut at the precisetime in order to ensure that the desired quantity of a given componentis actually dispensed into the mixing vessel. To many concretemanufacturers, the perceived cost of upgrading or properly calibratingtheir metering and dispensing equipment is higher than simplyoverdesigning the concrete, particularly since most manufacturers haveno idea how much the practice of overdesigning concrete actually costsand because it is thought to be a variable cost rather than a capitalcost.

Overdesigning often leads to the third cause of strength variability,which is overcementing. Overcementing involves increasing the amount ofhydraulic cement in an attempt to achieve or guarantee a minimumstrength by overcoming the effect on strength by randomly adding waterafter batching to adjust slump. This, however, can lead to increases instrength variability, as hardened cement paste is typically weaker as astructural element compared to the aggregate components. While addingmore cement may increase the binding strength provided by the cementpaste that holds the aggregates together, more cement can also weakenconcrete by displacing stronger aggregate materials with the weakercement paste as a structural component of the hardened concrete.Strength variability occurs as a result of the foregoing effects workingin opposite directions, but in differing amounts between differentbatches of concrete (e.g., due to differences in the water-to-cementratio, quality and characteristics of the hydraulic cement, aggregatesand water, and how the concrete is handled when delivered to a jobsite).

Overcementing can also cause microshrinkage, particularly on or near thesurface due to water evaporation, which reduces the strength anddurability of the concrete surface. Microshrinkage caused byovercementing and poor component distribution can cause cracks andcrazing within 1-2 years of manufacture. Overcementing can also causecreep, which is the dynamic (and usually undesirable) growth of concretemasses due to continued long term hydration and growth of hydrationproducts of the cement grains,

The fourth cause of concrete strength variability is the practice byconcrete truck drivers of adding water to concrete after batching in anattempt to improve or modify the concrete to make it easier to pour,pump, work, and/or finish. In many cases, concrete is uniformly designedand manufactured to have a standard slump (e.g., 3 inch) when theconcrete truck leaves the lot, with the expectation that the final slumprequested by the customer will be achieved on site through the additionof water. This procedure is imprecise because concrete drivers rarely,if ever, use a standard slump cone to actually measure the slump butsimply go on “look and feel”. Since adding water significantly decreasesfinal concrete strength, the concrete plant must build in acorresponding amount of increased initial strength to offset thepossible or expected decrease in strength resulting from subsequentwater addition. Because strength can be decreased by varying amountsdepending on the actual amount of water added by the driver, themanufacturer must assume a worst-case scenario of maximum strength losswhen designing the concrete in order to ensure that the concrete meetsor exceeds the required strength.

Given the foregoing variables, which can differ in degree and scope fromday to day, a concrete manufacturer may believe it to be more practicalto overdesign its concrete compositions rather than account and controlfor the variables that can affect concrete strength, slump and otherproperties. Overdesigning, however, is not only wasteful as aninefficient use of raw materials, sometimes providing concrete that issubstantially stronger than what is required can also be dangerous. Forexample, because stronger concrete is often more brittle than weakerconcrete, it can fail before the weaker concrete when subjected to theforces of an earthquake.

In an effort to more efficiently design concrete compositions and takeinto account variations in the particle size, particle sizedistribution, morphology, and packing densities of the various solidcomponents between different batches of cement and aggregates, theinventors previously developed a design optimization process thatgreatly improved upon traditional methods for designing concretemixtures. This process is described in U.S. Pat. No. 5,527,387 toAndersen et al., entitled “Design Optimized Compositions and ComputerImplemented Processes for Microstructurally Engineering CementitiousMixtures” (hereinafter “Andersen patent”). For brevity, the designoptimization process disclosed in the Andersen patent will be referredto as the “DOC program” (the term “DOC” being an acronym for “designoptimized concrete”).

The DOC program mathematically relates the properties of strength, slumpand other aspects, such as cost, cohesiveness and durability, based onthe concentrations and qualities of the various raw material inputs. TheDOC program is able to design and virtually “test” millions of differenthypothetical mix designs in seconds using a computer. This greatlyreduces the amount of time required to carry out trial-and-error testingthat would otherwise be necessary to identify a concrete mixture that isoptimized for strength, slump, cost and/or other desired features. Thegoal of the DOC program is to identify an optimal mix design, from amonga large number of hypothetical mix designs, based on such desiredfeatures as slump, strength, and cost. The DOC program fills in gapsinherent in standardized tables, which include a relatively small numberof mix designs given the variability of raw material inputs. The DOCprogram can design and virtually “test” millions of different mixdesigns, including those falling between the gaps of standardizedtables, in much less time than it takes to design and test one mixdesign using conventional trial-and-error methods.

First, the raw materials are carefully tested to determinecharacteristics that affect the slump, strength, cost, and/or otherdesired features of cementitious compositions made therefrom. Theseinclude, for example, the particle size and packing density of thevarious aggregate components (e.g., large, medium and small aggregates)and hydraulic cement particles, and the effect of one or more optionaladmixtures (e.g., fly ash, water reducers, fillers, etc.). Once the rawmaterials have been characterized with the required degree of accuracy,their characteristics are input into a computer used to carry out theoptimization process of the DOC program.

Thereafter, the DOC program designs a large number of hypotheticalconcrete mixtures, each having a theoretical slump and strength, byvarying the concentrations of cement, aggregate, water, and optionaladmixtures. The predicted slump and strength of each hypotheticalconcrete mixture is determined by inputting the variables (e.g., theconcentration and characteristics of the raw materials) into a system ofinterrelated mathematical equations. One of the equations utilized inthe DOC program is a variation of Feret's strength equation, whichstates that the compressive strength of the final hardened concretecomposition is proportional to the square of the volumetric ratio ofhydraulic cement to cement paste, which consists of cement, water andair:$\sigma = {K \cdot \left( \frac{V_{C}}{V_{C} + V_{W} + V_{A}} \right)^{2}}$

The constant “K” within this equation provides proper strength units andmagnitude. The strength equation can be modified as follows to predictthe strength of concrete that additionally includes other binders, suchas class F fly ash, as part of the cement paste:$\sigma = {K \cdot \left( \frac{V_{C} + {0.3\quad V_{FA}}}{V_{C} + {0.3\quad V_{FA}} + V_{W} + V_{A}} \right)^{2}}$

The DOC program can be carried out in an iterative manner in which eachiteration yields a hypothetical concrete mixture having a predictedslump and strength that is closer to the desired slump and strength thaneach previous iteration. In addition to slump and strength, the DOCprogram can optimize concrete for other desired features, such as cost,workability, or cohesion. Thus, in the case where a number of differentconcrete mixtures may have the desired slump and strength, the DOCprogram can identify which of the mixtures is “optimal” according to oneor more other criteria (e.g., cost, workability and/or cohesion).

Notwithstanding the foregoing, the DOC program, when initially invented,was based on the assumption, well-accepted in the art, that the constantK (or “K factor”) within Feret's strength equation is a true constantand does not vary as long as the same type of mixing apparatus andsource of raw materials are used each time. It has been well-accepted inthe art that if such variables are kept constant, the K factor remainsconstant regardless of variations in hydraulic cement concentration andconcrete strength. As a result of this well-accepted assumption, the DOCprogram required significant post-design corrections, even significanttesting and redesign of concrete compositions made using one or more ofthe “optimal” mix designs generated by the program. Thus, the inabilityof the DOC program to account for dynamic variability of the K factorlimited the practical application of an otherwise powerful designoptimization tool.

SUMMARY OF THE INVENTION

It has now been discovered that the constant K (or “K factor”) withinFeret's strength equation is not a constant but varies depending on theefficiency with which hydraulic cement is able to bind or glue theaggregate particles together. That is true even if the mixing apparatus,aggregate strength, and other factors that affect strength are keptconstant. The K factor, which dynamically varies with the bindingefficiency of the hydraulic cement binder, can be empirically determinedbased on concrete strength. Knowing the dynamic variability of the Kfactor allows for more accurate predictions of concrete strength whenperforming a design optimizing procedure compared to an optimizationprocedure that assumes the K factor remains constant so long as themixing apparatus and raw materials also remain constant. The inventiveoptimization procedure (hereinafter “improved DOC process”) efficientlyidentifies one or more optimized mix designs with less trial and errortesting since using the correct K factor in the first instance naturallyreduces the need to correct for errors that would otherwise arise byusing an incorrect K factor to predict concrete strength.

Although the binding efficiency of hydraulic cement, and therefore the Kfactor, cannot be readily measured directly, the K factor for a givenconcrete composition can be determined indirectly. By rearrangingFeret's equation, one can solve for K by knowing the compressivestrength, hydraulic cement volume and cement paste volume. By testing arange of standard concrete compositions sold by various manufacturersand then solving for K, the inventors surprisingly found that the Kfactor varied with actual concrete strength, more particularly, that theK factor of properly prepared concrete increased with increasingcompressive strength and follows a logarithmic curve. The logarithmiccurve has a theoretical limit corresponding to a concrete compositionhaving perfect component distribution and binding efficiency of thepaste system, which only occurs at very high strength (e.g., containingthe most optimal paste to aggregate ratio and a water-to-cement ratio ofabout 0.17 and having perfect distribution of paste and aggregatesthroughout the concrete composition). At lower strengths representativeof typical manufacturing needs and specifications, the K factor liesbelow the theoretical limit. This indicates that hydraulic cement is notable to realize its highest theoretical binding efficiency at lowerstrengths, but only approaches it at higher strengths.

Knowing how the K factor, and therefore the binding efficiency ofhydraulic cement, varies with strength greatly increases the accuracy bywhich an optimization procedure that utilizes an appropriate strengthequation can predict concrete strength for a large number ofhypothetical mix designs. On the other hand, the K factor is independentof changes in slump caused by changing water concentration and/orvariations in the size and/or morphology of aggregates. Using theforegoing principles regarding K factor, the improved DOC process canmore accurately identify one or more optimized mix designs from amongmany hypothetical mix designs. The improved DOC process efficientlyyields optimized concrete compositions that guarantee a specific minimumslump and strength at the lowest cost and with minimum variability dueto poor design. The improved DOC process is more efficient than theoriginal DOC program because knowing in advance how the K factor varieswith strength minimizes the amount of post design corrections (e.g.,through trial-and-error testing) that might otherwise be required.

One goal of the improved DOC process is to yield optimized mix designsthat substantially reduce concrete overdesign compared to conventionalmix designs used by concrete manufacturers. In one aspect of theinvention, the improved DOC process can be used to create one or moreoptimized mix designs that guarantee concrete having a specific minimumslump and strength while also reducing the wasted cost caused byoverdesign. Another aspect involves dynamically optimizing concrete mixdesigns based on feedback regarding variations in different batches ofraw materials. In yet another aspect, the improved DOC process can beused to re-design one or more existing mix designs of a concretemanufacturer. Identifying variations between the actual (or apparent)design K factor of an existing mix design and the optimal or theoreticalK factor corresponding to the design strength can be used to determinethe existence and degree of concrete overdesign. Improving the mixdesign to better utilize the hydraulic cement and optimize bindingefficiency of the cement paste can by itself reduce strength variabilityand the need to overdesign to account for such variability.

In addition to providing optimized mix designs, improving thecorrelation between predicted strength and actual strength can befurther enhanced by upgrading and/or recalibrating plant equipment tobetter ensure that a manufacturer is able to accurately measure anddispense the raw materials used to manufacture concrete. Such upgradesmay not be economically practical in the case where a plant uses poormix designs. Perfectly calibrated equipment cannot manufacture concretethat is any better than a poor mix design will allow. The use ofoptimized mix designs therefore allows the manufacturer to obtain thefull benefit of any capital equipment upgrades. Because improving plantequipment alone may not yield much benefit, and because optimized mixdesigns cannot by themselves overcome variability imparted by faultyequipment, improving plant equipment and optimizing mix designs allowsboth improvements to realize their full potential, thus indicating asynergistic relationship.

In one embodiment, the present invention provides improved methods fordesigning and manufacturing optimized concrete mix designs utilizing astrength equation that employs a unique K factor value, which varies andis selected depending on the inherent efficiency of component use of theresulting concrete composition (e.g., as empirically predicted by thedesired minimum, or “design strength”), all other things being equal.Knowing how the K factor varies with concrete strength greatly improvesthe ability to accurately and efficiently design an optimized concretecomposition because it reduces or minimizes variability between designand actual strength. Minimizing variability between the design strengthand actual strength reduces the amount of trial-and-error testing thatmight otherwise be required to identify a concrete mix design that istruly optimized for slump and strength at minimum cost.

As compared to conventional methods for designing concrete usingstandardized tables, the improved DOC process more precisely considersthe actual characteristics of raw materials utilized by a concretemanufacturer. Standardized tables only roughly approximate actual slumpand strength because the characteristics of raw materials presumed inthe tables rarely, if ever, reflect the true characteristics of rawmaterials actually used by a concrete manufacturer. Each concretemanufacturing plant utilizes raw materials that are unique to thatplant, and it is unreasonable to expect standardized tables toaccurately account for materials variability among different plants. Theimproved DOC process is able to virtually “test” mix designs that moreaccurately reflect the raw materials actually utilized by the plant at agiven time. By accounting for variations in the quality of rawmaterials, the improved DOC process is able to substantially reduce thedegree of overdesigning of concrete compositions that might otherwiseoccur using standardized mix design tables and methods.

Another aspect of the invention involves the redesigning of one or morepre-existing mix designs used by a manufacturing plant to manufactureits commercial concrete compositions. In one embodiment, the methodfirst involves, as a threshold matter, determining whether and by howmuch an existing concrete composition is overdesigned. Every concretecomposition has a design strength, which is typically determined by theminimum strength that must be guaranteed for that composition, and anactual strength that can be measured by properly preparing concreteunder absolute controls based on the mix design and testing itsstrength. Because of the tendency of manufacturers to overdesign toaccount for expected strength variabilities from batch to batch, therecan be a substantial difference between the apparent design K factorbased on the guaranteed minimum strength of a concrete mix design andthe actual or “true” K factor based on the actual strength of theconcrete when properly manufactured according to the mix design.

The extent to which an existing concrete mix design is overdesigned canbe ascertained by: (1) properly preparing a concrete test sampleaccording to the existing mix design; (2) allowing the concretecomposition to harden; (3) measuring the actual strength of the hardenedconcrete composition; and (4) comparing the actual strength of theconcrete composition with the design strength of the existing mixdesign. The amount by which the actual strength deviates from the designstrength corresponds to the degree by which the existing mix design isoverdesigned. The foregoing process requires an amount of time that isnecessary for the concrete composition to cure sufficiently in order toaccurately measure actual strength.

The degree of overdesign can alternatively be determined in a moreexpedited fashion by: (1) determining an apparent design K factor of theexisting concrete mix design based on the design strength and ratio ofcomponents within a concrete composition made according to the existingmix design; (2) identifying an optimal theoretical K factorcorresponding to the design strength; and (3) comparing the apparentdesign K factor of the existing concrete mix design with the optimal Kfactor that corresponds to the design strength. The amount by which theapparent design K factor deviates from the optimal K factor correspondsto the degree by which the existing mix design is overdesigned.Knowledge of how the optimal K factor varies with concrete strength cantherefore be used as a diagnostic tool to determine whether and by howmuch a pre-existing mix design is overdesigned without waiting for aconcrete test sample to harden.

After determining that a pre-existing mix design is overdesigned, anoptimized concrete mix design can be designed using the improved DOCprocess. After selecting a design strength representing the guaranteedspecified minimum strength, a revised or corrected K factorcorresponding to the design (or desired) strength is selected and usedin the improved DOC process. An iterative optimization process utilizingone or more algorithms, including Feret's equation employing the reviseddesign K factor, designs and virtually tests a number of hypotheticalconcrete compositions in order to identify one or more mix designsoptimized for a specified minimum strength and slump having the lowestcost or other desired factors. An optimized mix design reducesvariability between design strength and actual strength compared to thepre-existing concrete mix design, thereby reducing overdesign and costof the resulting concrete composition. By correctly readjusting therelative concentrations of the various components, the improved DOCprocess improves the binding efficiency of the hydraulic cement binderand reduces how much cement is required to ensure the specified strengthrequirement. Overcementing can be greatly reduced or eliminated.

In summary, by utilizing correct K factors selected based on designstrength, the improved DOC program can accurately and efficientlyredesign each standard pre-existing concrete mix design utilized by themanufacturing plant in order to improve the binding efficiency of thecement binder. This reduces or eliminates overdesigning and reducescost. An existing concrete manufacturing plant can be upgraded simply byproviding optimized concrete mix designs even without upgrading and/orrecalibrating the manufacturing plant equipment.

Variations between actual strength and design strength can be furtherminimized by properly controlling the preparation and handling of theconcrete compositions. Some retooling may be necessary to ensure thatthe batching and weighing equipment meets standard ASTM-94 requirements.Thus, according to another aspect of the invention, affirmative stepscan be taken to better control the measuring and dispensing of thecomponents used to manufacture concrete. According to one embodiment,the components are preferably weighed or measured with an accuracy ofabout ±2.0%, more preferably with an accuracy of about ±1.0%, and mostpreferably with an accuracy of about ±0.5%. The amount of water includedin the concrete composition is carefully controlled so that it does notsignificantly change from the time the composition is first made withinthe concrete truck and when it is used at the job site. In order toprevent decreases in actual strength due to human error, on-site slumpadjustments can be made to wet concrete compositions through the use ofspecial admixtures instead of by increasing the water content.

In order to account for all water inputs, the moisture content of thesolid components (e.g., hydraulic cement and aggregates) can becontinuously monitored using moisture sensors (e.g., microwave sensorsthat measure absorption of microwave energy by any moisture present).Through an information feed-back mechanism, which can be advantageouslycontrolled by a computer, the amount of batch water that is added to themixing vessel can be varied to account for variations in the moisturecontent of the solid components. In this way, the total water contentwithin a batch of concrete can be more accurately controlled, therebyreducing variations in strength and/or slump that might otherwise occur.

In some cases it may be desirable to quickly redesign an alreadyoptimized mix design in order to adjust the slump without significantlychanging the strength. This can be done without creating a whole new mixdesign from scratch. To maintain the same strength, while varying theslump, the same water-to-cement ratio of the paste is maintained, andonly the volume of paste is altered to adjust slump. Adding more pasteto a design optimized concrete composition increases slump, while addingless paste decreases slump. Thus, the overall ratio of paste toaggregate is adjusted to change the slump. Because the water-to-cementratio of the paste remains the same, the strength remains essentiallythe same according to Feret's equation. In some cases, the ratio of fineto coarse aggregates may remain the same. In other cases, this ratio canbe altered somewhat depending on the desired effect on other propertiesof altering the ratio of paste to aggregate (e.g., cohesiveness,durability, etc.). Once the concentrations of the various componentshave been adjusted to provide the correct slump, the overall yield canbe corrected by adjusting the quantities of the aggregates to provide adesired volume of concrete.

Each of the foregoing embodiments, individually and collectively,contribute to a reduction in concrete strength variability, includingdifferences between design and actual strength and also differences instrength between different batches made using the same mix design. Byreducing or eliminating large differences between design and actualstrength, and/or strength variability between different batches ofconcrete, the inventive methods and systems greatly reduce theoverdesign of concrete.

Like the DOC program disclosed in the Andersen patent, the improved DOCprocess can be implemented, at least in part, using a computing system(i.e., a computer) in order to design and virtually test a large number(e.g., thousands or millions) of hypothetical mix designs in arelatively short time period in order to identify one or more mixdesigns that are optimized based on desired criteria (e.g., strength,slump and cost). Briefly stated, the improved DOC process is able todesign and virtually “test” different mix designs by altering therelative concentrations of all the raw materials and then calculating,using one or more algorithms (e.g., those set forth in the Andersenpatent), the slump and strength of each virtual concrete compositionmade according to each hypothetical mix design. The improved DOC processthen identifies one or more optimized mix designs having the desiredslump and strength. Afterwards, test samples are made to determineactual slump and strength. If the slump differs, changes in slump can bemade by increasing or decreasing the concentration of cement paste. Thestrength can be kept the same by maintaining the same water to cementratio in the cement paste. The strength can be altered by changing thewater-to-cement ratio.

As with the original DOC program, the improved DOC process can beembodied by a computer program product comprising a computer-readablemedium (e.g., a physical storage device, such as a hard drive, memorydevice, magnetic tape or disk, optical storage media, or other knowndigital storage device) that contains executable instructions forcarrying out the computer-implemented aspects of the inventive method.

Because each manufacturing plant has its own unique set of raw materialsand/or processing inputs and/or blend efficiencies (i.e., no two plantsuse exactly the same combination of raw materials and possess the exactsame equipment calibrated and/or operated in the exact same manner), itwill be appreciated that each manufacturing plant produces concretecompositions having unique aspects that are specific to a givenmanufacturing plant. In other words, even if two manufacturing plantsuse the same standardized mix designs (i.e., recipes), the concretedelivered by each plant will, in same way, be unique to each plant. Thatmeans that pre-existing concrete mix designs that have been modified andoptimized utilizing the improved DOC program will yield new concretecompositions that are themselves unique in that they will have neverbeen manufactured at any time anywhere in the world. Thus, improvedconcrete compositions manufactured using optimized mix designs resultingfrom the implementation of the improved DOC process are themselvesunique and therefore novel as between all previously manufacturedconcrete.

It turns out that every concrete composition that is made has its ownunique signature design K factor and also an actual K factor that can bedetermined by testing the actual strength of the composition. That istrue both before and after implementation of the improved DOC process.However, after implementation of the improved DOC process, the signatureK factors, both design and actual, for an optimized concrete compositionof a manufacturing plant will exceed the signature K factors, bothdesign and actual, of a pre-existing non-optimized concrete compositionthat was redesigned or replaced using the improved DOC process. Byknowing and comparing the design and/or signature K factors of both apre-existing and an optimized concrete composition of a givenmanufacturing plant, one can readily ascertain whether a particularconcrete composition produced by the manufacturing plant wasmanufactured using the pre-existing mix design or an optimized mixdesign designed using the improved DOC process. Thus, the signature Kfactor can be used as a diagnostic tool to distinguish whether anon-optimized or overdesigned concrete composition or an optimizedconcrete composition was used in a building project (i.e., to determinewhether or not the improved DOC process has been implemented by aconcrete manufacturer in designing its concrete compositions).

These and other advantages and features of the present invention willbecome more fully apparent from the following description and appendedclaims, or may be learned by the practice of the invention as set forthhereinafter.

BRIEF DESCRIPTION OF THE DRAWINGS

To further clarify the above and other advantages and features of thepresent invention, a more particular description of the invention willbe rendered by reference to specific embodiments thereof which areillustrated in the appended drawings. It is appreciated that thesedrawings depict only typical embodiments of the invention and aretherefore not to be considered limiting of its scope. The invention willbe described and explained with additional specificity and detailthrough the use of the accompanying drawings, in which:

FIG. 1 is a chart that includes K factor curves that illustrate how theK Factor changes as a function of the compressive strength of concrete;

FIG. 2 is a chart that demonstrates how the actual K Factors of knownconcrete compositions deviate from K factors along an optimal K Factorcurve, which illustrates the degree by which such compositions areoverdesigned;

FIG. 3 is another chart showing how the actual K Factors of knownconcrete compositions deviate from K factors along an optimal K Factorcurve, which illustrates the degree by which such compositions areoverdesigned;

FIG. 4 is a schematic diagram that illustrates a computing system bywhich design optimization, re-designing, and other aspects of theinvention may be carried out;

FIG. 5 is a flow chart that illustrates an exemplary optimizationprocess according to the invention for designing an optimized concretemixture;

FIG. 6A is a packing density chart for the ternary mixture of cement,quartz sand (0-2 mm), and crushed granite (8-16 mm);

FIG. 6B is the packing density chart of FIG. 6A with lines designatinghow to read a composition corresponding to a density within the chart;

FIG. 6C is a graph of a packing density chart showing pseudo particlelines;

FIG. 7 illustrates an exemplary slump correction chart used to correctslump when approximating the particle packing densities of the solidcomponents.

FIGS. 8A-8B comprise a logic flow diagram of the optimization system.

FIG. 8C is a tree of the logic flow diagram shown in FIG. 8B.

FIG. 9 is a flow chart that illustrates an exemplary computerimplemented iterative optimization process according to the invention;

FIG. 10 is flow chart that illustrates an exemplary optimization processaccording to the invention for designing an optimized concrete mixturewhich accounts for changes in the K Factor as compressive strengthvaries;

FIG. 11 is a flow chart that illustrates an exemplary process formanufacturing a concrete composition from an optimized concrete mixdesign in order to ensure that the actual strength closely correlates tothe desired or predicted strength;

FIG. 12 is a flow chart that illustrates an exemplary abbreviatedre-design process for changing the slump of an optimized concrete mixdesign without substantially changing the strength;

FIG. 13 is a flow chart that illustrates an exemplary process forredesigning a pre-existing concrete mix design by employing a correctunderstanding of the K Factor and how it varies as a function ofconcrete compressive strength; and

FIG. 14 is a flow chart that illustrates an exemplary process forupgrading an existing concrete manufacturing plant by employing acorrect understanding of the K Factor and how it varies as a function ofconcrete compressive strength.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

I. Introduction

The present invention utilizes a design optimization process, which isat least in part computer-implemented, that identifies one or moreoptimized concrete mix designs that are optimized relative to, e.g.,strength, slump and cost. The design optimization process is able toaccount for variability in raw material inputs and design an optimizedconcrete compositions based on variations in raw material qualities. Itdoes this by effectively designing and testing large numbers (e.g.,thousands or millions) of hypothetical concrete mixtures at least inpart by means of a computer-implemented process in order to identify oneor more mix designs having optimal properties. This process greatlyreduces or eliminates the need for extensive trial-and-error testing,which is both expensive and time consuming. Moreover, unlike Shilstoneoptimization, the improved DOC program is able to account for particlesize variations among different batches of raw materials and also costoptimize.

The terms “yard” and “cubic yard” are used interchangeably throughoutthis application and shall refer to the typical volumetric unit ofconcrete sold in the United States. This quantity can readily beconverted into metric units by known conversion factors that convertyard into meters, centimeters, or other desired metric units. By way ofexample, one cubic yard is equal to 0.76455486 cubic meters.

II. Relationship of K Factor to Concrete Strength

An important feature of the invention is the understanding that Feret'sconstant K (or “K” factor) is not actually a constant but is relatedlogarithmically to concrete strength. That means that increasing theamount of hydraulic cement within an optimized composition not onlyincreases concrete strength by virtue of the increased amount of binder,which would be expected, but also improves the binding effectiveness orefficiency of the paste. Thus, the increase in strength of concrete asmore hydraulic cement is added to an optimized concrete compositionexceeds the strength that would be predicted by Feret's equation if theK factor were actually a constant for all strengths. Whereas it wasknown that the K factor changed depending on mixing apparatus andaggregate type and strength, it was heretofore believed that the Kfactor remained constant for all strengths as long as the same rawmaterials and mixing apparatus were used.

The term “Feret's equation” refers to the following equation, whichpredicts concrete strength based solely on the volume of hydrauliccement, water and air in the concrete mixture:$\sigma = {K \cdot \left( \frac{V_{C}}{V_{C} + V_{W} + V_{A}} \right)^{2}}$

For purposes of disclosure and the appended claims, the term “Feret'sequation” shall also refer to the following modified Feret's equation,which predicts concrete strength based on the volume of hydrauliccement, class F fly ash, water, and air in the concrete mixture:$\sigma = {K \cdot \left( \frac{V_{C} + {0.3\quad V_{FA}}}{V_{C} + {0.3\quad V_{FA}} + V_{W} + V_{A}} \right)^{2}}$

As can be seen from this version of Feret's equation, certain types offly ash contribute to concrete strength but not to the same degree ashydraulic cement. Moreover, although the volume of fly ash is shownmultiplied by a fly ash constant 0.3, it may sometimes be appropriate touse a different fly ash constant (e.g., ranging from 0.3-0.6) dependingon the type of fly ash used. This substitution can be carried out bythose of skill in the art when appropriate, and such modification shallalso constitute “Feret's equation”.

In general, the term “Feret's equation” shall refer to other similarvariations that may be constructed so long as they at least relate thepredicted compressive strength of the concrete composition to the ratioof hydraulic cement volume to cement paste volume (i.e., hydrauliccement, other binders, water and air) in the concrete mixture (e.g., theuse of silica fume, which can contribute to strength).

The term “K factor” includes modifications of the exemplary K factorsdisclosed herein required to convert the calculated strength fromEnglish units (i.e., pounds per square inch or “psi”) to metric units(e.g., MPa). As is well-known to those of skill in the art, 1 MPa=145psi. The term “K factor” shall include other modifications necessarywhen altering Feret's equation, as discussed above.

It should be appreciated that the K factor is not an absolute number andis not always the same for all different types of concrete compositionsand/or apparatus used by manufacturing plants to manufacture concrete.In fact, each manufacturing plant will have its own unique K factorcurve depending on the type and quality of aggregates, the type andquality of hydraulic cement used, and the type and quality of mixingapparatus. The K factor curve will typically move up or increase withincreasing mixing efficiency, aggregate strength, hydraulic cementstrength, and other factors that systematically contribute to concretestrength.

So long as system inputs remain essentially the same, the K factor curvefor a particular manufacturing plant can, at least in theory, bedetermined by identifying a single K factor point along the K factorcurve and then constructing a logarithmic curve that passes through thatpoint. Once an inappropriate K factor curve has been constructed for aparticular manufacturing plant, the curve can be used to design andpredict concrete strengths for a wide variety of different concretesproduced by that manufacturing plant.

It should also be understood that there are different K factorsdepending on the context in which that term is used. The term “design Kfactor” refers to the K factor that is utilized within the improved DOCprocess of the present invention in order to design and virtually “test”a large number (e.g., millions) of different hypothetical mix designs inorder to identify one or more of such mix designs that are “optimal”with respect to strength, slump, cost and other desired factors. Thedesign K factor will, of course, vary depending on the design strength,or guaranteed minimum strength, of a particular concrete composition.For a given set of raw materials inputs and processing equipment, therewill typically be a single design K factor curve.

The terms “optimal K factor” and “true K factor” refer to K factorsfound along an optimal K factor curve that represents perfectly designedand mixed concrete by a manufacturing plant utilizing a given set of rawmaterials available. Thus, the “optimal” or “true” K factor can varybetween different manufacturing plants and is therefore not an absolutenumber. Nevertheless, for a given set of raw material inputs, thereexists perfectly designed and manufactured concrete for which theoptimal or true K factor can theoretically be used to predict strength.Because manufacturing plants and personnel cannot produce perfectconcrete every time, there will typically be some degree of overdesign,however slight, to account for such variability. Thus, the design Kfactor will typically differ from (e.g., be lower than) the optimal trueK factor for that given set of raw materials. Notwithstanding suchvariation, the design K factor used to make a well optimized concretecomposition will much more closely correlate to the optimal or true Kfactor than compared to apparent design K factors corresponding to lessoptimized or non-optimized concrete compositions.

The term “apparent design K factor” refers to the K factor that can beascertained for a preexisting concrete composition that may not haveitself been designed using a K factor. Even if a K factor is not used todesign a concrete composition, it nevertheless can be assigned anapparent design K factor based on what K factor would have been used todesign such concrete using the disclosed optimization procedures. In thecase of a poorly optimized or overdesigned concrete composition, theapparent design K factor will deviate significantly from the optimal ortrue K factor. The apparent design K factors of such compositions willdeviate much more than the design K factors of well optimized concretemade using the same inputs. The apparent design K factor is determinedbased on the design strength (i.e., minimum guaranteed strength) and mixdesign of the preexisting concrete composition.

The term “actual K factor” shall refer to the K factor that isdetermined by mixing up a concrete composition according to a given mixdesign, allowing the concrete to cure, measuring the compressivestrength of the concrete, and then calculating the actual K factor basedon actual strength and quantity of components within the concretecomposition. For a properly prepared concrete composition, the actual Kfactor will exceed the design K factor since the design K factortypically accounts for variations in concrete strength.

A graphic representation of how the K factor varies with the compressivestrength of concrete is depicted in FIG. 1. FIG. 1 actually includes twocurved lines following a logarithmic curve corresponding to twodifferent K factors that have been determined by the inventors. Thelower K factor curve corresponds to concrete compositions made utilizinghydraulic cement, water, aggregate and other standard admixtures used inthe art. The upper K factor line corresponds to hydraulic cementcompositions that additionally include an amine strengthener. The Kfactors used to generate the lines shown in FIG. 1 were determined byanalyzing a wide variety of standard mix designs utilized inmanufacturing plants in various parts of the United States or variationsthereof (e.g., that use a strengthening amine). In general, the K factorcan be calculated according to the following rearrangement of Feret'sequation for compositions that include hydraulic cement, water, andaggregate:$K = \frac{\sigma}{\left( \frac{V_{C}}{V_{C} + V_{W} + V_{A}} \right)^{2}}$

The strength variable σ corresponds to the actual strength that wasdetermined for various concrete compositions ranging in strength from500 psi to 8,000 psi. For concrete compositions that also include flyash, the K factor can be determined according to the followingrearrangement of a modified Feret's equation:$K = \frac{\sigma}{\left( \frac{V_{C} + {0.3\quad V_{FA}}}{V_{C} + {0.3V_{FA}} + V_{W} + V_{A}} \right)^{2}}$

The increased K factor corresponding to increased strength according tothe upper line shown in FIG. 1 can be obtained by utilizing an amineknown as “THEED” (i.e., tetrahydroxydiethylenediamine, also known asethanol, 2, 2′, 2″, 2″′-(1,2-ethanediyldnitrolo)tetrakis-). In order toobtain increased strength, and therefore a higher K factor, it ispreferable to utilize up to about 0.5% of THEED, more preferably up toabout 0.25%, and most preferably up to about 0.1%. Once it has beenunderstood that the K factor varies logarithmically with concretecompressive strength, one of skill in the art, using techniquesdescribed or readily ascertained from the current disclosure, can modifythe exemplary K factor shown in FIG. 1 to account for variations basedon different concentrations of THEED.

FIG. 1 further demonstrates that the “optimal” or “theoretical” Kfactors are not absolute or lie along an absolute fixed curve that isthe same regardless of the inputs and mixing apparatus of the concretecomposition. Adding an amine strengthener raises the K factor (and Kfactor curve representing all K factors for that system) based on theincreased strength of the resulting concrete even though the ratio ofhydraulic cement to paste remains the same. The same would be true forother admixtures or alterations in composition such that there could bea unique or representative K factor curve for every unique set of rawmaterials inputs. The same would be true for different types of mixingapparatus which might cause the cement paste to behave in unique waysspecific to that mixing apparatus or methodology. In general, the effectof mixing efficiency on K factor is more dramatic with increasing cementcontent and strength (i.e., mixing becomes more crucial when thepotential binding efficiency of hydraulic cement is maximized). What thegraph at FIG. 1 shows is that for any fixed set of compositional and/orprocessing variables, the K factor follows a logarithmic curve relativeto compressive strength. That means the effectiveness of the hydrauliccement, more precisely the cement paste, as a binder that holds or gluesthe aggregates together decreases with decreasing strengths. It alsoincreases with increasing strength towards a theoretical limit beyondwhich no further increase in binding effectiveness is possible (i.e.,where the binding efficiency is as high as theoretically possible, withthe limit of cement paste strength being at stoichiometric levels ofwater and cement and wherein the components are perfectly mixed. Thisdoes not mean, however, that the K factor necessarily increases withincreasing hydraulic cement concentration. Many manufacturers engage inthe practice of overcementing in an attempt to increase or maximizestrength, sometimes with disastrous results as the concrete composition,if not properly optimized to accommodate a huge cement increase (e.g.,doubling), might undergo severe microshrinkage cracking and crazing inthe short run and also excessive creep or expansion in the long run.

What the K factor curves illustrated in FIG. 1 essentially depict arethe optimal K factors for a given set of raw materials inputs. Thedesign K factor used in an optimization procedure may be the same or maydeviate from the optimal K factor to guarantee a specific minimumstrength and slump. Because some variability between design strength andactual strength is possible, even in the case of highly optimizedconcrete compositions, some amount of deviation between the design Kfactor used and the optimal K factor can be tolerated to account forsome expected variation. What should be understood is that there is lessvariation between the design strength and the actual strength of a welloptimized mix design compared to a poor mix design. In other words, theactual strength of concrete compositions made using optimized mixdesigns will more closely corresponding to design strength than concretecompositions made from a poor mix designs. As a result of this, anoptimized mix design made according to the inventive design optimizationprocess will have a signature design K factor that exceeds the design Kfactor of a poor mix design. Similarly, because the binding efficiencyof cement paste in a well-designed concrete composition typicallyexceeds the binding efficiency of cement paste in a poorly designedconcrete composition, the actual K factor of a well-designed concretecomposition would also be expected to exceed the actual K factor of apoorly-designed concrete composition. This concept becomes moreunderstandable with reference to FIGS. 2 and 3.

The apparent design K factor for each specific mix design shown in FIGS.2 and 3 can be determined by inputting values for cement, water, air anddesign strength into Feret's equation and then solving for K. The actualK factors that lie along the K factor curve can be derived by properlypreparing a number of concrete compositions using standard optimized mixdesigns used by a plurality of manufacturers according to ASTM C-94 orother rigorous standards known in the art, measuring the actual strengthof the concrete test sample, and then solving for K. An optimal K factorcurve can be prepared by plotting measured K factors based on optimallyprepared concrete compositions against the corresponding compressivestrengths.

In many cases, the actual strength of a concrete test sample made from apre-existing concrete mix design may substantially exceed the designstrength, thereby indicating that the pre-existing concrete mix designis overdesigned. However, this alone does not provide a precise way toredesign the pre-existing concrete mix design to reduce or eliminatesuch overdesigning. Using a revised design K factor that more closelycorresponds to the optimal K factor within an optimization procedurethat utilizes Feret's equation facilitates the ability to redesign thepre-existing mix design in order for actual strength to more closelycorrespond to design or predicted strength.

In order to demonstrate the degree by which standard concrete mixdesigns used in the industry are overdesigned in several existingconcrete manufacturing plants (and therefore have an excessively lowdesign K factor), reference is now made to FIGS. 2 and 3. FIG. 2 shows avariety of data points corresponding to apparent design K factors thatwere determined for each of a plurality of standard mix designs utilizedby TXI, Tarmac, TTM, VM, Elmhurst, and Kaneville. The amount by whichthe data points deviate from the optimal K factor line shown in FIG. 2indicates the degree to which such standard mix designs are or wereoverdesigned relative to their design strengths.

The design K factors shown in the data points below the optimal K factorline in FIG. 2 were determined utilizing a rearranged Feret's equationand solving for K, wherein the strength σ corresponds to the design orpredicted strength rather than the actual strength of the concretecompositions manufactured according to such mix a designs. In everycase, the predicted or design strength was far less than the actualstrength when the compositions were properly manufactured. The amount bywhich the tested compositions were found to be overdesigned represents apotential cost savings if such mix designs could be redesigned accordingto the inventive methods disclosed herein. For example, it is currentlyestimated that redesigning so as to better optimize existing concretemix designs can save between $4 and $10 per yard of concretemanufactured. Considering that concrete manufacturers typically enjoy aprofit of only about $1 to $2 per yard, the estimated cost savings aretremendous and represent a substantial improvement in the art ofconcrete manufacture.

FIG. 3 compares the apparent design K factors for a number ofpre-existing concrete mix designs of various manufacturing plants usingin manufacturing concrete compositions that either include substantialentrained air or are substantially free of entrained air. Again, thedeviation between the data points representing the apparent design Kfactors and the optimal K factor curve shown in FIG. 3 graphicallyillustrates the potential cost savings if the pre-existing mix designswere redesigned and optimized according to the inventive methodsdisclosed herein.

As will be readily appreciated, by comparing the apparent design Kfactor of an existing concrete mix design with the optimal K factor fora given compressive strength lying on the curve shown in FIGS. 1-3, onemay readily ascertain the degree by which an existing concrete mixdesign and corresponding concrete composition are overdesigned. Thus,knowing the optimal K factor and how it varies with compressive strengthcan be employed as a diagnostic tool to test whether the mix designs andconcrete compositions of a concrete manufacturing plant are optimized orwhether they are significantly overdesigned. Once it has been determinedthat an existing mix design is overdesigned, the mix design can beredesigned using the improved DOC process in order to identify one ormore optimized mix designs having the desired slump and strength atlower cost. Because the improved DOC process takes into account theactual raw material inputs available to the manufacturer, it is betterable to optimize the concrete mixtures compared to standardized tables,which typically cannot account for variations in raw materials inputsamong different manufacturing plants or between batches. The improvedDOC program understands the dynamic relationship between optimal Kfactor and concrete strength, which allows it to more efficientlyidentify one or more optimized mix designs compared to the original DOCprogram described in the Andersen patent.

III. Computer-Based Operating Environment

The operating environment for performing embodiments of the improved DOCprogram may comprise a special purpose or general-purpose computer,including various types of computer hardware, as discussed in greaterdetail below. FIG. 4 is a schematic diagram illustrating an exemplarycomputing system 100 that may be used to implement features of thepresent invention. The described computing system is only one example ofsuch a suitable computing system and is not intended to suggest anylimitation as to the scope of use or functionality of the invention.Neither should the invention be interpreted as having any dependency orrequirement relating to any one or combination of components illustratedin FIG. 4.

Computing systems are now increasingly taking a wide variety of forms.Computing systems may, for example, be handheld devices, appliances,laptop computers, desktop computers, mainframes, distributed computingsystems, or even devices that have not conventionally considered acomputing system. In this description and in the claims, the term“computing system” is defined broadly as including any device or system(or combination thereof) that includes at least one processor, and amemory capable of having thereon computer-executable instructions thatmay be executed by the processor. The memory may take any form and maydepend on the nature and form of the computing system. A computingsystem may be distributed over a network environment and may includemultiple constituent computing systems.

Referring to FIG. 4, in its most basic configuration, a computing system100 typically includes at least one processing unit 102 and memory 104.The memory 104 may be system memory, which may be volatile,non-volatile, or some combination of the two. An example of volatilememory includes Random Access Memory (RAM). Examples of non-volatilememory include Read Only Memory (ROM), flash memory, or the like. Theterm “memory” may also be used herein to refer to non-volatile massstorage such as physical storage media. Such storage may be removable ornon-removable, and may include, but is not limited to, PCMCIA cards,magnetic and optical disks, magnetic tape, and the like.

As used herein, the term “module” or “component” can refer to softwareobjects or routines that execute on the computing system. The differentcomponents, modules, engines, and services described herein may beimplemented as objects or processes that execute on the computing system(e.g., as separate threads). While the system and methods describedherein may be implemented in software, implementations in hardware, andin combinations of software and hardware are also possible andcontemplated.

In the description that follows, embodiments of the invention aredescribed with by reference to acts that are performed by one or morecomputing systems. If such acts are implemented in software, one or moreprocessors of the associated computing system that performs the actdirect the operation of the computing system in response to havingexecuted computer-executable instructions. An example of such anoperation involves the manipulation of data. The computer-executableinstructions (and the manipulated data) may be stored or instantiated inthe memory 104 of the computing system 100.

Computing system 100 may also contain communication channels 108 thatallow the computing system 100 to communicate with other computingsystems over, for example, network 110. Communication channels 108 areexamples of communications media. Communications media typically embodycomputer-readable instructions, data structures, program modules, orother data in a modulated data signal such as a carrier wave or othertransport mechanism and include any information-delivery media. By wayof example, and not limitation, communications media include wiredmedia, such as wired networks and direct-wired connections, and wirelessmedia such as acoustic, radio, infrared, and other wireless media. Theterm computer-readable media as used herein includes both storage mediaand tangible communications media (i.e., sending and receiving deviceswhich can temporarily store executable instructions, but not theelectronic signals themselves).

Embodiments within the scope of the present invention also includecomputer-readable media for carrying or having computer-executableinstructions or data structures stored thereon. Such computer-readablemedia can be any available media that can be accessed by a generalpurpose or special purpose computer. By way of example, and notlimitation, such computer-readable media can comprise physical storageand/or memory media such as RAM, ROM, EEPROM, CD-ROM or other opticaldisk storage, magnetic disk storage or other magnetic storage devices,or any other medium which can be used to carry or store desired programcode means in the form of computer-executable instructions or datastructures and which can be accessed by a general purpose or specialpurpose computer. When information is transferred or provided over anetwork or another communications connection (either hardwired,wireless, or a combination of hardwired or wireless) to a computer, thecomputer properly views the connection as a computer-readable medium.Thus, any such connection is properly termed a computer-readable medium.Combinations of the above should also be included within the scope ofcomputer-readable media.

Computer-executable instructions comprise, for example, instructions anddata which cause a general purpose computer, special purpose computer,or special purpose processing device to perform a certain function orgroup of functions. Although the subject matter has been described inlanguage specific to structural features and/or methodological acts, itis to be understood that the subject matter defined in the appendedclaims is not necessarily limited to the specific features or actsdescribed herein. Rather, the specific features and acts describedherein are disclosed as example forms of implementing the claims.

IV. Overview of Exemplary Design Optimization Process

According to a currently preferred embodiment, computer-implementeddesign optimized processes according to the invention can utilize atleast some of the features disclosed in U.S. Pat. No. 5,527,387 toAndersen et al. (“Andersen patent”), the disclosure of which isincorporated by reference. An important difference is that the presentinvention accounts for the fact that the K Factor utilized in Feret'sequation is not a true constant but varies logarithmically with thecompressive strength of concrete. In other words, it has now beendiscovered that increasing the concentration of hydraulic cement in anoptimized mixture (as opposed to overcementing) increases itseffectiveness or binding efficiency. The concept that the K Factorvaries with concrete strength was not previously known and was thereforenot appreciated in the Andersen patent or incorporated in the originalDOC program (though the original DOC program worked as designed andintended).

When implementing the improved DOC process, the design K Factor utilizedin Feret's equation to determine design strength is selected based onthe specific minimum slump and strength of concrete that must beguaranteed by the manufacturer. In many other respects, the improved DOCprocess can be implemented in a manner similar that the original DOCprogram disclosed in the Andersen patent. It should be understood,however, that it is within the scope of the invention to utilize any setor series of known algorithms for designing one or more concrete mixdesigns so long as the design K factor that is used when calculatingstrength according to Feret's equation varies with changes in thedesired or target strength (e.g., increases logarithmically withconcrete strength).

FIG. 5 is a flow chart that schematically illustrates or outlinesvarious steps that may be performed according to an embodiment of theinvention. These steps are similar to those disclosed in the Andersenpatent, except that the procedure illustrated in FIG. 5 selects and thenutilizes a design K factor based on the specific minimum strength andslump requirement when calculating the design strength of eachhypothetical concrete mix design generated by the improved DOC process.Thus, notwithstanding the similarity that may exist between the processsteps illustrated in FIG. 5 and those disclosed in the Andersen patent,the process of FIG. 5 was not known in the prior art as embodied herein.The twelve steps are summarized as follows:

-   -   Step 1: Ascertaining the maximum packing density and        corresponding composition of a dry concrete mixture having        cement and one or more types of aggregate;    -   Step 2: Utilizing a K factor corresponding to the desired or        design strength, determining the initial optimal concrete        mixture that is closest to the maximum packing density and has a        desired strength, slump, and cohesion at a specific        fine-to-coarse-aggregate ratio;    -   Step 3: Utilizing a K factor corresponding to the design        strength, designing various optimal mixtures and comparing the        unit cost for each optimal mixture at defined        fine-to-coarse-aggregate ratios so as to determine the overall        optimal mixture with respect to cost;    -   Steps 4-7: Calculating the effects of individually combining        different admixtures including fly ash, silica fume, water        reducers, or fillers, respectively, to identify one or more        optimal concrete mixtures;    -   Step 8: Determining the best optimal mixture having desired        properties and minimal cost for mixtures that include fine        aggregate, cement, coarse aggregate, mixing water, and two or        more admixtures selected from fly ash, silica fume, and water        reducers;    -   Step 9: Modifying the resulting mixture to insure that it        reflects the proper concentration of air-entraining agent so as        to have the proper air content;    -   Step 10: Utilizing a correction factor to further optimize the        results of the preceding steps and ensure proper slump;    -   Step 11: Adjusting porosity if necessary to insure that the        selected mixture has sufficient durability for its intended use;        and    -   Step 12: Accurately determining the volume or weight of the        various components of a mixture needed to produce a desired        concrete yield.

The foregoing steps outlined above and depicted in FIG. 5 will now bedescribed with more particularity.

A. Step 1: Ascertaining Maximum Packing Density

Step 1 includes ascertaining the maximum packing density of a dryconcrete mixture for a given set of raw materials (i.e., cement and oneor more types of aggregate). A detailed description of an exemplaryembodiment for determining a ratio of hydraulic cement and one or moretypes of aggregates that maximizes particle packing density is set forthin the Andersen patent at col. 18, line 1-col. 25, line 5. Variousmethods, including measuring techniques and mathematical algorithms, fordetermining particle size and packing density for each of the rawmaterials inputs are described in this section of the Andersen patent.The discussion at col. 18, line 1-col. 25, line 5 of the Andersen patentdescribes exemplary acts that may be used to carry out step 1.

Initially, each of the aggregate and cement components are defined bytheir respective average diameter size (d′) and natural packing density(φ). These values may be experimentally determined and can be used tocalculate the theoretical packing density of a theoretical concretecomposition. The average diameter size is determined using knownmethods, such as by plotting the particle size distribution of eachmaterial according to the Rosin-Rammler-Sperling-Bennett distributiondescribed by the equation:R(D)=exp{−(d/d′)^(n)}

Where, d is the particle diameter, R(D) is the cumulative probabilitythat the diameter is less than d, d′ is the diameter for whichR(d′)=0.368 corresponding to 36.8% residue on that sieve size, and n isthe slope of the line defined by plotting the percent of particlesretained on a sieve versus the sieve size.

The packing density of each type of material, φ, is determined byfilling the material into a cylinder having a diameter of at least 10times the largest particle diameter of the material. The cylinder isthen tapped against a hard surface until the material is fullycompacted. By reading the height of compacted material in the cylinderand the weight of material, the packing density is calculated accordingto the formula: $\varphi = \frac{W_{M}}{{SG}_{M} \cdot V_{M}}$

Where,

W_(M)=weight of the material,

SG_(M)=specific gravity of the material, and

V_(M)=volume of the material.

In this way, not only is the volume of particles quantified but it isdone as a function of particle morphology, specific surface area andother specific surface characteristics.

The maximum packing density of a conventional, three-component mixtureincluding cement, one type of fine aggregate, and one type of coarseaggregate is determined by incrementally varying the volume of eachcomponent in the mixture and calculating the corresponding packingdensity. The various packing densities are then plotted on atriangular-shaped packing density chart so as to determine whatcomposition has the maximum packing density. By way of example, FIG. 6Ais a packing density chart for a ternary mixture of cement, quartz sand(0-2 mm), and crushed granite (8-16 mm). Side (A) of the chart definesthe volume percent of fine aggregate (sand); side (B) defines the volumepercent of cement; and the bottom or side (C) defines the volume percentof coarse aggregate (crushed granite). The values inside the trianglerepresent the packing density at various percent volume mixtures of thecomponents. The chart may be read in the following manner:

Sub-step 1(a): Select a desired packing density from within thetriangle. By way of example, point “Z” is selected on FIG. 6B whichrepresents the maximum packing density for the defined mixture.

Sub-step 1(b): Determine the percent volume of cement used in theconcrete mixture needed to obtain the packing density at point “Z” bydrawing a horizontal line 20 from point “Z” to side (B) of the triangle.The value defined by where line 20 and side (B) of the triangleintersect is the percent volume of cement needed to obtain the desiredpacking density. In the example on FIG. 6B, the percent volume cement isapproximately 10%.

Sub-step 1(c): Determine the percent volume of fine aggregate in themixture by drawing a line 22 parallel to side (B) of the triangle, theline starting from point “Z” and intersecting side (A) of the triangle.The value defined at where line 22 and side (A) intersect is the percentvolume of fine aggregate needed to obtain the desired packing density.In the example, the percent volume of fine aggregate is approximately30%.

Sub-step 1(d): Since the percent volume of the mixture must sum to 100%,it logically follows that if the mixture is 10% cement and 30% fineaggregate, the percent volume of coarse aggregate must be 60%. Thisvalue, however, can also be determined from the packing density chart bydrawing a line 24 parallel with side (A), the line starting at point “Z”and intersecting side (C). The value at the intersection of line 24 andside (C) corresponds to the percent volume of coarse aggregate. As shownin FIG. 6B, the value turns out to be approximately 60%. Using thismethod, the composition can be ascertained for any packing density onthe chart or, using the reverse operation, the packing density can beascertained for any desired composition.

The packing density values within the chart are evaluated from theToufar, Klose, and Born model (hereinafter “Toufar model”) used inconnection with a correction factor. The Toufar model is a formula forcalculating the packing densities of binary mixtures:$\phi = \frac{1}{\frac{r_{1}}{\phi_{1}} + \frac{r_{2}}{\phi_{2}} - {r_{2} \cdot \left( {\frac{1}{\phi_{2}} - 1} \right) \cdot \frac{d_{2} - d_{1}}{d_{1} + d_{2}} \cdot \left\{ {1 - \frac{1 + {4 \cdot \frac{r_{1}}{r_{2}} \cdot \frac{\phi_{2}}{\phi_{1} \cdot \left( {1 - \phi_{2}} \right)}}}{\left\lbrack {1 + {\frac{r_{1}}{r_{2}} \cdot \frac{\phi_{2}}{\phi_{1} \cdot \left( {1 - \phi_{2}} \right)}}} \right\rbrack}} \right\}}}$

Where,

-   -   r₁=volume of smaller particles,    -   r₂=volume of larger particles,    -   d₁=diameter of smaller particles,    -   d₂=diameter of larger particles,    -   φ₁=packing density of the smaller particles, and    -   φ₁=packing density of the larger particles.

Other models may also be used for calculating the packing densities ofbinary mixtures. Examples of applicable models are the Aim model and theLarrard model discussed in the article Johansen, V. and Andersen, P. J.,“Particle Packing and Concrete Properties” 118-122, Materials Science ofConcrete II (The American Ceramic Society, Inc., 1991), the teachings ofwhich are incorporated by reference. Additional discussion regardingpacking density, including the use of pseudo-particles to deternminepacking densities using the Toufar model for ternary mixtures, is setforth in the Andersen patent.

In an alternative embodiment, the average particle size d′ is determinedfor each component using known methods, but instead of actuallymeasuring the packing density φ, the packing density φ for eachcomponent is assumed to be either 0.5, 0.55 or 0.6, since solidparticles typically have a particle packing density ranging from 0.5 to0.6. The optimization program may then be carried out using theexemplary steps discussed below, with the proviso that the actual slumpis likely to vary from the theoretical or predicted slump due tovariations between true packing density and the assumed packing density.As a result, a final correction step for slump is performed at or nearthe end of the process (e.g., as part of Step 10 discussed below).Because slump can be measured the moment a concrete mixture is prepared,unlike strength, slump corrections are not time consuming. A slumpcorrection curve, as exemplified by FIG. 7, can be prepared by preparingtwo concrete mixtures having higher and lower slumps, plotting the highand low slumps (e.g., 5 cm and 15 cm) against the correspondingconcentration of water in volume % for the two concrete mixtures, andthen drawing a straight line between the two points. The water volumecorrelating to any desired slump is shown on the curve (e.g., thecorrelation indicated by the dotted line). A final mix design having adesired slump can be prepared by utilizing an amount of water shown onthe slump curve corresponding to the desired slump.

As part of the improved DOC program, the average particle size d′measured for each solid component and the particle packing density foreach solid component, whether measured or estimated, are input into acomputing system. These values affect the properties that are laterdetermined for each of the plurality of mix designs that are created.The particle size and particle packing densities permit the computersystem, by virtue of one or more interrelated algorithms, tohypothetically “test” the resulting properties of each virtual concretecomposition based on the mix designs that are created as part of thedesign optimization process.

B. Step 2: Property Optimization

Step 2 involves determining an initial concrete mixture that is closestto the maximum packing density determined in Step 1 and that has thedesired strength, slump, and optionally cohesion at a specificfine-to-coarse aggregate ratio. A detailed description of an exemplaryembodiment of a process for identifying a concrete mixture that isoptimized with respect to strength, slump and optionally cohesion is setforth in the Andersen patent at col. 25, line 8-col. 29, line 10. Theterm “cohesion” refers to the tendency of the concrete composition toresist segregation and bleeding. Various methods including mathematicalalgorithms for optimizing a concrete mixture with respect to strength,slump and optionally cohesion are described in this section of theAndersen patent. The discussion at col. 25, line 8-col. 29, line 10 ofthe Andersen patent describes exemplary acts that may be used to carryout step 2.

In sub-step 2(a), an initial mixture that is sufficiently close to themaximum packing density to optimize concrete properties withoutsegregating or bleeding is selected by first, as discussed in Step 1,locating the maximum packing density on the packing density chart andthe corresponding volume composition. The volume of the correspondingcement, fine aggregate, and coarse aggregate at the point of maximumpacking are respectively defined by the variables V_(C(MP)), V_(F(MP)),and V_(CA(MP)), which add up to 1.0. Next, the volume of cement is heldconstant while the volume of fine aggregate is increased by a quantitydefined as the cohesion safety factor, and the volume of coarseaggregate is decreased by the same quantity. The mixture is thus movedhorizontally left on the packing density chart. The correspondingmixture is defined as the initial mixture.

The volume (V) of the components in the initial mixture are defined bythe equations:V _(C) =V _(C(MP))V _(F) =V _(F(MP)) +CFV _(CA) =V _(CA(MP)) −CF

Wherein, the variable CF represents the cohesion safety factor and istypically about 0.05. The cohesion safety factor insures that themixture has sufficient fine aggregate to make a cohesive mixture thatwill not segregate or bleed. Mixtures to the right of the initialmixture on the packing density chart will typically segregate or bleed.The cohesion safety factor can vary in a range between about 0 to about0.15 depending on the type of concrete. A lower strength concretetypically requires a higher cohesion factor up to about 0.15, while ahigher strength concrete requires a lower cohesion factor of less thanabout 0.05.

The fine-to-coarse-aggregate ratio of the initial mixture is defined bya pseudo-particle line extending from the apex of the packing densitychart, through the position of the initial mixture, and to the coarseaggregate line (FIG. 6C; compare FIGS. 6A-6B). The following sub-stepsare presented as an example of how to ascertain the optimal concretemixture along this defined pseudo-particle line.

In sub-step 2(b), the packing density of the composition of the initialconcrete mixture is determined as described in Step 1.

In sub-step 2(c), the amount of mixing water required to provide theinitial concrete mixture with a predetermined desired slump isascertained. Determining this amount of water is a two-step process.First, the amount of water needed to provide the mixture with a 1 cmslump is determined using the following formula:$W_{1} = {\frac{1}{\phi} - 1}$

Where, φ=the packing density of the mixture, as defined in sub-step2(b), and

W₁=the volume of water required to give the mixture a 1 cm slump. Thevalue for W₁ is a fraction of the volume of the solids in the mixture.

Once W₁ is calculated for a 1 cm slump, the amount of water needed forthe desired slump is calculated using Popovic's formula as follows:$W_{2} = \frac{W_{1}}{\left( \frac{S_{1}}{S_{2}} \right)^{0.1}}$

Where, W₁=the volume of water needed for a 1.0 cm slump as previouslydefined,

W₂=the volume of water needed to give the mixture a desired slump,

S₁=1.0, representing 1.0 cm slump (correct exponent actually found to be0.085 by the inventors), and

S₂=the desired slump in centimeters.

In sub-step 2(d), using the results from sub-steps 2(a)-2(c),calculating the 28-day compressive strength of the resulting mixtureusing Feret's equation:$\sigma = {K \cdot \left( \frac{V_{C}}{V_{C} + V_{W} + V_{A}} \right)^{2}}$

Where, σ=theoretical 28-day compressive strength of the concrete mixturein MPa,

V_(C)=volume of cement in the mixture,

W₂=volume of water, defined in Step 2(c), needed to give the mixture thedesired slump,

K=Feret's constant, which is now discovered to vary with compressivestrength σ as illustrated in FIGS. 1-3, and

V_(A)=the volume of air in the mixture and is defined by the followingequation:$V_{A} = {\left( \frac{1 + W_{2}}{1 - \frac{\%\quad{AIR}}{100}} \right) - 1 - W_{2}}$

Where AIR is the estimated percent volume of air in the mixture. Thevolume of air in a mixture varies based on the type of mixer used, thevolume of fine aggregate in the mixture, and the types of admixturescombined with the mixture. The percent volume of air can be estimated bythose skilled in the art and is generally between about 1% to 2% for aslump greater than 10 cm and between about 2% to 4% for slump less than10 cm.

In sub-step 2(e), the resulting compressive theoretical strength, σ, iscompared with the desired strength. If the theoretical strength of themixture is less than the desired strength, sub-steps 2(b)-2(e) arerepeated by replacing the initial mixture with a new mixture andcorresponding new packing density. The composition of the new mixture isobtained by increasing or decreasing the volume of cement in order toobtain the desired strength. An estimate of the volume of cement neededto obtain the desired strength is determined by inputting the desiredstrength into Feret's equation and solving for the corresponding volumeof cement according to the following equation: $\begin{matrix}{V_{C{(N)}} = {\left( {\frac{1 + W_{2}}{1 - \frac{\%\quad{AIR}}{100}} - 1} \right) \cdot \frac{\left( \frac{\sigma_{D}}{K} \right)^{0.5}}{\left( {1 - \frac{\sigma_{D}}{K}} \right)^{0.5}}}} & (16)\end{matrix}$

Where, V_(C(N))=volume of cement in the new mixture,

W₂=volume of water needed to obtain the desired slump in the initial orprevious mixture,

% AIR=estimated percent volume of air in the mixture,

K=Feret's constant, which varies with concrete strength, and

σ_(D)=the desired strength in MPa.

As the volume of cement changes for the new mixture, the volume of fineaggregate and coarse aggregate must be normalized so that the volume offine aggregate, coarse aggregate, and cement sum up to 1.0. However, theratio of fine-to-coarse-aggregate remains constant. Accordingly, thevolume of fine aggregate and coarse aggregate in the new mixture aredefined by the equations:V _(F(N)) =r _(F)·(1−V _(C(N)))V _(CA(N)) =r _(CA)·(1−V _(C(N)))

Where, r_(F) and r_(CA) are the ratios of fine aggregate and coarseaggregate, respectively, and are constants for each pseudo-particleline. The ratios are defined by the equations:r _(F) =V _(F)/(V _(F) +V _(CA))r _(CA) =V _(CA)/(V _(F) +V _(CA))

This new mixture corresponds to the position on the packing densitychart defined by the intersection of the pseudo-particle line describedin sub-step 2(a) and a horizontal line extending from new volume ofcement determined by equation (16) above. As the volume of cementchanges, one moves up or down on the pseudo-particle line. Sub-steps2(b)-2(d) are continually repeated until the theoretical strength of themixture equals the desired strength and the resulting mixture for thedefined fine-to-coarse-aggregate ratio has the desired slump andstrength using a minimal amount of cement and water. Typically, thedesired mixture is found within ten iterations.

C. Step 3: Cost Optimization

Step 3 involves comparing the unit cost of various optimal mixtures atdefined fine-to-coarse-aggregate ratios so as to determine one or moreoverall optimized mixture(s) that are also optimized in terms of lowcost. A detailed description of an exemplary embodiment for identifyinga concrete mixture that is optimized with respect to cost, while alsohaving the desired strength and slump, is set forth in the Andersenpatent at col. 29, line 13-col. 30, line 42, which constitute exemplaryacts for carrying out step 3.

According to one embodiment, this may be accomplished by firstcalculating the unit cost of the initial optimal mixture determined inStep 2. An optimal composition and resulting unit price is thendetermined for a second optimal mixture defined by a newfine-to-coarse-aggregate ratio. The new fine-to-coarse-aggregate ratiois obtained by decreasing the percent volume of coarse aggregate by 1%and increasing the percent volume of fine aggregate, respectively. Theunit price of the second optimal mixture is then compared with the unitprice of the initial mixture. If the price of the initial mixture isless than the price of the second mixture, the composition of theinitial mixture is the most economical and the process is over. If thesecond mixture is less than the price of the initial mixture, thefine-to-coarse-aggregate ratio is again varied so as to obtain a thirdoptimal mixture. The cost comparison is then repeated until the leastexpensive mixture is obtained.

The combination of Steps 1-3 provides exemplary methods for designing amixture of cement, water, and aggregate having a desired strength andslump. The amount of water added to the mixture can be minimized tomaximize strength. The proportions of fine aggregate, coarse aggregate,and cement can be optimized to minimize the cost of the mixture.Furthermore, using the above process, mixtures having desired propertiescan be consistently and accurately produced independent of thevariations in the feedstock. Steps 1-3 can also be used to determine themixture of highest durability. As will be discussed later in Step 11,the mixture with highest durability is defined as the mixture with thelowest possible total porosity. This is because, in general, as theporosity increases the durability of the mixture decreases. Studies havedetermined that the porosity of a mixture decreases as the packingdensity increases. Thus, mixtures closest to the maximum packing densitywould be predicted to generally have the highest durability.

Steps 4-7 provide additional optimization possibilities by optionallycalculating the individual effects of combining different admixtures,such as fly ash, silica fume, water reducers, or fillers, within aconcrete mixture.

D. Step 4: Determining Effect of Fly Ash

A detailed description of an exemplary embodiment for identifying anoptimal concrete mixture that includes fly ash is set forth in theAndersen patent at col. 30, line 44-col. 33, line 63. This section ofthe Andersen patent includes exemplary mathematical algorithms relatingto the use of fly ash and exemplary acts corresponding to Step 4.

In general, the process includes first repeating Steps 1 and 2 so as todetermine the optimal mixture (without an admixture) having desiredstrength and slump properties for a defined fine-to-coarse-aggregateratio. Based on the composition of the resulting optimal mixture, apercent volume of cement is incrementally replaced with fly ash. As thepercent volume of fly ash is increased, the unit price of each mixtureis calculated and compared to the previous mixture to determine theleast expensive mixture for the defined fine-to-coarse-aggregate ratio.

The fine-to-coarse-aggregate ratio is then varied by moving 1% to theleft on the packing density chart. The above process is then repeated todetermine the least expensive mixture using fly ash with the newfine-to-coarse-aggregate ratio. The unit price for the optimal mixturesat the different fine-to-coarse-aggregate ratios are then compared todetermine the least expensive mixture. The process continues to move tothe left on the packing density chart until the overall optimal mixturehaving fly ash and the desired properties is obtained. An exemplaryalgorithm that accounts for the effect of fly ash on slump involves thefollowing modified Popovic's equation:$W_{2} = {\frac{W_{1}}{\left( \frac{S_{1}}{S_{2}} \right)^{0.1}} - W_{FA}}$

Where, W_(FA) is a reduction, as a result of the fly ash, in the volumeof water needed to produce a mixture with a desired slump and isdetermined by the equation:$W_{FA} = \frac{{W_{1} \cdot \%}\quad{{FA} \cdot 6}}{100 \cdot 37}$

Where, W₁=the volume of mixing water required for a 1.0 cm slump in astandard mixture as previously defined, and

% FA=the percent volume of fly ash in the combination of fly ash andcement.

The value for W₂ can then be used to calculate the 28 day strength usinga modified version of Feret's equation that accounts for the fly ash,such as:$\sigma = {K\left( \frac{V_{C} + {K_{2}V_{FA}}}{V_{C} + {K_{2}V_{FA}} + W_{2} + V_{A}} \right)}^{2}$

Where K₂ is a constant for fly ash, and typically ranges between 0.3 and0.6.

E. Step 5: Determining Effect of Silica Fume

A detailed description of an exemplary embodiment for identifying anoptimal concrete mixture that includes silica fume (aka, fumed silica)is set forth in the Andersen patent at col. 33, line 65-col. 35, line40. This section of the Andersen patent includes exemplary mathematicalalgorithms relating to the use of silica fume and exemplary actscorresponding to Step 5.

The optimal mixture using silica fume can be ascertained in the samemanner used in determining the proper amount of fly ash in Step 4.However, the formulas for the required amount of water and resultingstrength are different. In contrast to fly ash, silica fume requiresmore water for a given slump, but silica fume imparts a greater strengthto the cement mixture. With regard to the packing density chart, thevolume of silica fume is also considered as part of the volume of cementin the mixture. If desired, a pseudo particle can be used to representthe combination of the cement and silica fume. An exemplary algorithmthat accounts for the effect of fumed silica on slump involves thefollowing modified Popovic's equation:$W_{2} = {\frac{W_{1}}{\left( \frac{S_{1}}{S_{2}} \right)^{0.1}} + W_{SF}}$

Where, W_(SF) is an increase, as a result of the silica fume, in thevolume of water needed to produce a mixture with a desired slump and isdetermined by the equation:$W_{SF} = \frac{{W_{1} \cdot \%}\quad{{SF} \cdot 20}}{100 \cdot 20}$

Where, % SF=the percent volume of silica fume in the combination ofsilica fume and cement.

The value for W₂ can then be used to calculate the 28 day strength usinga modified version of Feret's equation that accounts for the fumedsilica, such as:$\sigma = {K\left( \frac{V_{C} + {K_{3}V_{SF}}}{V_{C} + {K_{3}V_{SF}} + W_{2} + V_{A}} \right)}^{2}$

Where, K₃=a reactivity constant describing the strength development pervolume of silica fume comparable to the same volume of cement.Typically, this value is between 1.5 and 4, with 2 being the preferredvalue. The actual value can be empirically determined for a given silicafume.

F. Step 6: Determining Effect of Water Reducers

A detailed description of an exemplary embodiment for identifying anoptimal concrete mixture that includes water reducers is set forth inAndersen et al. at col. 35, line 45-col. 37, line 55. This section ofthe Andersen patent includes exemplary mathematical algorithms relatingto the use of water reducers and exemplary acts corresponding to Step 6.

Assuming that only water reducers are added to a standard concretemixture, the process for obtaining the optimal mixture is the same asthat used for Step 4 to obtain an optimal mixture using fly ash. Theonly difference is that the formulas for determining the required amountof mixing water and the resulting strength are modified. The processincludes determining the optimal mixture for the firstfine-to-coarse-aggregate ratio. Incremental amounts of water reducersare then added to the mixture. The unit cost of these mixtures arecalculated and compared so as to determine the optimal mixture havingwater reducers at the initial fine-to-coarse-aggregate ratio. Thefine-to-coarse-aggregate ratio is then varied and the process isrepeated. By comparing the unit cost for the optimal mixtures at eachfine-to-coarse-aggregate ratio, the overall optimal mixture using waterreducers can be determined.

Based on the parameters of the standard water reducer, the percentvolume of water needed to produce a mixture including a water reducerwith a desired slump is determined by the following equation:$W_{2} = {\frac{W_{1}}{\left( \frac{S_{1}}{S_{2}} \right)^{0.1}} - W_{WR}}$

Where, W_(WR) is a reduction, as a result of the water reducer, in thevolume of water needed to produce a mixture with a desired slump and isdetermined by the equation:$W_{WR} = \frac{{{W_{1} \cdot \%}\quad{WR}} - 30}{100\quad(2)}$

Where, W₁=the volume of mixing water required for a 1.0 cm slump aspreviously defined, and

% WR the percent quantity of water reducer in the mixture by weight ofthe cement.

The value for W₂ can then be used to calculate the 28-day strength usingFeret's equation. As water reducers do not independently contribute tothe strength of concrete, the same formulas used in Step 2 can be usedfor calculating 28-day strength and for estimating the volume of cementneeded to obtain the desired strength. Since the amount of waterrequired for the desired slump is decreased by using a water reducingagent, the water-cement ratio in the mixture is decreased, thereby,increasing the strength of the resulting mixture. Accordingly, theamount of cement can be reduced until a mixture is defined possessingthe desired strength and slump and having the initial 0.1% waterreducing agent. A cost comparison is then performed and if the mixturewith the water reducer is cheaper, an additional 0.1% water reducer isadded to the mixture. The above process is then again repeated accordingto the format described in Step 4 for fly ash until the optimal mixtureincluding a water reducer is determined.

G. Step 7: Determining Effect of Fillers

A detailed description of an exemplary embodiment for identifying anoptimal concrete mixture that includes fillers (e.g., finely groundrock) is set forth in Andersen et al. at col. 37, line 57-col. 38, line59. This section of the Andersen patent includes exemplary mathematicalalgorithms relating to the use of fillers and exemplary actscorresponding to Step 7.

Fillers generally do not possess cementitious properties and, thus, donot directly contribute to the strength of the resulting concrete.Similar to fly ash, however, fillers do decrease the amount of mixingwater required to obtain a desired slump as compared to cement and,accordingly, can indirectly affect the slump and strength of theresulting concrete. By way of example and not by limitation, fillers caninclude calcium carbonate, dolomite, granite, basalt, and ore that arecrushed to have a particle size similar to fly ash—diameters less than100 μm. The reduction in the amount of water need to obtain a desiredslump is a result of the approximately spherical shape of certainfillers and the lack of hydraulic activity. An exemplary algorithm thataccounts for the effect of fillers on slump involves the followingmodified Popovic's equation:$W_{2} = {\frac{W_{1}}{\left( \frac{S_{1}}{S_{2}} \right)^{0.1}} - W_{F}}$

Where, W_(F) is a reduction, as a result of the filler, in the volume ofwater needed to produce a mixture with a desired slump and is determinedby the equation:$W_{F} = \frac{{W_{1} \cdot \%}\quad{{FIL} \cdot 6}}{100\quad(37)}$

Where, % FIL=the percent volume of filler in the combination of fillerand cement.

The value for W₂ can then be used to calculate the 28 day strength. Asfillers do not independently contribute to the strength of the concrete,the same formulas used in Step 2 can be used for calculating 28 daystrength and for estimating the volume of cement needed to obtain thedesired strength.

H. Step 8: Combined Design Optimization System

A detailed description of an exemplary embodiment for determining thecombined effect of adding two or more admixtures to a concrete mixdesign (e.g., two or more of fly ash, silica fume, and water reducer) isset forth in the Andersen patent at col. 38, line 61-col. 43, line 13.This section of Andersen et al. includes exemplary mathematicalalgorithms relative to identifying an optimal concrete mixture thatutilizes multiple admixtures, as well as acts corresponding to step 8.

Once the process is understood of how to optimize a concrete mixtureusing a single admixture in conjunction with cement, fine aggregate,coarse aggregate and water, the various processes can be combined into asystem using an embedded “do loop” that allows one to determine theoptimal mixture having selective combinations of admixtures, theadmixtures including fly ash, silica fume and water reducers. Thisprocess essentially accounts for the effects on slump, strength, costand other desired factors when utilizing two or more admixtures. In oneaspect, the following exemplary modified Feret's equation can beutilized that accounts for two or more admixtures (e.g., fly ash andsilica fume) within the cement paste and their affect on strength:$\sigma = {K\left( \frac{V_{C} + {K_{2}V_{FA}} + {K_{3}V_{SF}}}{V_{C} + {K_{2}V_{FA}} + {K_{3}V_{SF}} + W_{2} + V_{A}} \right)}^{2}$

Where,

-   -   V_(SF)=% SF·(V_(T)/100)    -   V_(FA)=%, FA·(V_(T)/100)    -   V_(C)=V_(T)−V_(SF)−V_(FA)

Where, V_(T)=the total volume of cement, silica fume, and fly ash in themixture. The other variables are as previously and defined in Step 4 and5.

The following equation defines the amount of water required to give amixture including fly ash and silica fume a desired slump:$W_{2} = {\frac{W_{1}}{\left( \frac{S_{1}}{S_{2}} \right)^{0.1}} - W_{FA} + W_{SF}}$

Where, W_(SF) and W_(FA) are as defined in Steps 4 and 5.

The logic of the optimization procedure may be employed in Step 8 asdepicted in the logic flow diagram shown in FIGS. 8A and 8B and thelogic tree shown in FIG. 8C. FIGS. 8A-8C schematically illustrateexemplary acts corresponding to Step 8. In many ways, the process issimilar to previous steps, except that fly ash and silica fume onlydisplace a portion of the hydraulic cement. As a result, thefine-to-coarse aggregate ratio does not need to be varied in this step.What are varied as the various ratios of cement, aggregates, fly ash andsilica fume to determine an mix design that is optimized to cost andthat includes two or more of fly ash, silica fume and a water reducer.

Should the desired strength not equal the calculated strength, theestimated values for the new volumes of cement, fly ash, and silica fumecan be calculated from the following equations, respectively:$V_{C{(N)}} = \frac{\left( \frac{\sigma_{D}}{K} \right)^{05}\frac{W_{2} + V_{\Lambda}}{1 - \left( \frac{\sigma_{D}}{K} \right)^{0.5}}}{1 + \frac{{K_{2} \cdot \%}\quad{FA}}{100 - {\%\quad{FA}}} + \frac{{K_{3} \cdot \%}\quad{SF}}{100 - {\%\quad{SF}}}}$$V_{{FA}{(N)}} = \frac{\%\quad{{FA} \cdot V_{C{(N)}}}}{100 - {\%\quad{FA}}}$$V_{{SF}{(N)}} = \frac{\%\quad{{SF} \cdot V_{C{(N)}}}}{100 - {\%\quad{SF}}}$

Where all variables are as previously defined in Steps 4 and 5.

Finally, as discussed in relation to step 6, the addition of waterreducers is only taken into consideration in determining the amount ofwater required to give a mixture a desired slump. Accordingly,independent of whether the water reducer is to be added to thecombination of cement and fly ash, cement and silica fume, or thecomposition of cement, fly ash and silica fume, the above definedequations are only varied by subtracting the reduction in the amount ofwater required for a desired slump as a result of the addition of thewater reducer.

For example, the required amount of water for a desired slump in amixture containing cement, fly ash, silica fume, water reducer, fineaggregate, and coarse aggregate is determined by the following equation:$W_{2} = {\frac{W_{1}}{\left( \frac{S_{1}}{S_{2}} \right)^{0.1}} - W_{FA} + W_{SF} - W_{WR}}$

Where, the values for W_(FA), W_(SF), and W_(WR) are as defined in Steps4, 5, and 6, respectively.

It should also be noted that the affects of other pozzolans oradmixtures can also be added to the optimization process by simplyadding another loop to the iterative process. Similarly, fillers couldhave been added to the above system, but since fillers are seldom (ifever) added to a mixture including other admixtures, the result wouldhave been the same.

I. Step 9: Modifications Using Air Entraining Agent

Step 9 involves optionally modifying the concrete mixture using anair-entraining agent, if necessary, to ensure that the concretecomposition has a proper air content. A detailed description of anexemplary embodiment for employing air-entraining agents, if necessaryor desired, is set forth in the Andersen patent at col. 43, line 15-col.44, line 13. This section of the Andersen patent includes exemplary actscorresponding to Step 9.

Unlike the admixtures discussed above, air-entraining agents are notmodeled into the optimization process and thus must be corrected afterthe fact. Air-entraining agents are admixtures that stabilize bubblesformed during the mixing process by lowering the surface tension of thewater. The air-entraining agent forms a water repelling film that issufficiently strong to contain and stabilize air bubbles. Unlikenaturally occurring air bubbles, air bubbles formed through the use ofan air-entraining agent are extremely small and have a diameter sizeranging from about 10 to about 1000 μm. Benefits to increasing thepercent volume of entrained air voids in concrete are the improvedresistance to freezing and thawing of hardened concrete in moistconditions and the increased workability of the unhardened concretemixture.

Once the optimal mixture is actually produced, the actual air content inthe mixture can be determined. If the air content for a given slumpafter completion of the optimization process is too low or too highcompared to the assumed air content used in sub-step 2(c), theoptimization process can be recalculated using the corrected value forthe content of air or the mixture can be reformed with the appropriateamount of air-entraining agent. The air content can also modeledaccording to the discussion in Step 10 below. As with water reducers,the percent volume of an air entraining agent in a mixture is typicallyso small that the agent itself is not taken into account as affectingthe volume of the mixture. However, the resulting amount of airincorporated into the mixture is taken into consideration in determiningthe strength of the mixture.

J. Step 10: System Correction Factor

Step 10 identifies and implements a system correction factor to ensurethat the final concrete composition has the desired slump. A detaileddescription of an exemplary embodiment for correcting slump if necessaryis set forth in the Andersen patent at col. 44, line 17-col. 45, line32. This section of Andersen et al. includes exemplary mathematicalalgorithms relative to correcting slump and exemplary acts correspondingto Step 10.

Once the iterative process of Step 8 is completed, a linear regressionanalysis can be used to improve the accuracy of the system results. Thismay be accomplished by plotting the theoretically determined amount ofmixing water required to obtain a desired slump versus the actual amountmixing water required to obtain a desired slump. The relationshipbetween the plotted values is then defined and incorporated intoPopovic's formula so as to increase the accuracy of the theoreticalamount of water required to obtain a desired slump. In practice, theabove process includes the following sub-steps:

Sub-step 10(a): Determining the theoretical amount of water required toobtain a desired slump in the optimal mixture defined in Step 8. Thisamount corresponds to the value for W₂ solved from Popovic's formula andis the amount used in determining the resulting 28-day strength of theoptimal mixture.

Sub-step 10(b): Physically combine the theoretical amount of water withthe optimal concrete mixture of Step 8. Next, experimentally determinethe actual slump and air content of the mixture. As a result ofapproximations incorporated into the optimization process, there willoften be a discrepancy between the actual values for slump and air andthe theoretical values for slump and air.

Sub-step 10(c): Using Popovic's formula, solve for the amount of water,W₂, needed to give the defined mixture the actual slump determined insub-step 10(b). Sub-steps 10(b) and 10(c) now give the actual andtheoretical amounts of water, respectively, required to give a specificmixture a specific slump.

Sub-step 10(d): Repeat Steps 10(a)-10(c) for different desired slumps.The steps should be repeated at least three times with the accuracy ofthe final results improving the more the steps are repeated. Thisprovides two sets of values corresponding to the actual and theoreticalamounts of water required to obtain a defined slump.

Sub-step 10(e): Plot the values of Step 10(d) with the actual amount ofwater required for a specific slump on the y-axis and the theoreticalamount of water required for a specific slump on the x-axis. Studieshave shown that such a plot will reveal a linear relationship.

Sub-step 10(f): Define the linear relationship of Step 10(e) in thefollowing form:W _(2c)=(W ₂ ·m)+b

Where,

W_(2c) actual amount of water for a defined slump (in use, the valuerepresents the corrected theoretical amount of water for a definedslump),

W₂=theoretical amount of water for a defined slump,

m=slope of the plot in Step 10(e), and

b=the y intercept.

Sub-step 10(g): Plot the experimentally determined air content valuesfor each the mixtures versus the experimentally determined slump valuesfor the corresponding mixtures. Define the correlation in the followingform:AIR_(ACT)=(SLUMP·m)+b

Where,

AIR_(ACT)=the volume of air in a mixture based on the correspondingslump,

SLUMP=the slump for a given mixture,

m=slope of the plot of actual slump versus correspond air content, and

b=the y intercept of the slope.

Sub-step 10(h): The formula of sub-step 10(f) is then incorporated intothe design optimization process such that after the theoretical amountof mixing water required for a desired slump is solved for fromPopovic's formula, the resulting value for W₂ is input into equationdescribed for sub-step 10(f) above. W_(2c) is then solved for providingan improved or corrected value for the amount of water required toobtain a desired slump. The desired slump is then incorporated into theequation described in sub-step 10(g) to obtain the volume of air in themixture. The resulting volume of air and corrected water volume are thenused in Feret's equation to solve for the strength of the mixture. Theoptimization process then continues as previously discussed. In this waythe slump can be estimated to within ±2 cm.

K. Step 11: Ensuring Sufficient Durability

Step 11 ensures the concrete composition has sufficient durability forits intended use. A detailed description of one currently preferredembodiment for ensuring sufficient durability, if necessary or desired,is set forth in that Andersen patent at col. 45, lines 34-60. Thissection of Andersen et al. includes an exemplary mathematical algorithmrelating to porosity, which affects durability, and describes actscorresponding to Step 11.

The above optimization process can also be used to insure that theselected concrete composition has sufficient durability for its intendeduse. Durability is the ability of a concrete structure to maintain itsintegrity over an extended period of time and is measured in this patentin terms of porosity. Mixtures with a high porosity typically have anexcessively high concentration of water or fine aggregate and as suchhave low durability. Total porosity of a mixture can be determined bythe following equation, where it is assumed 80% of the hydration of thecement has already occurred:${{TOTAL}\quad{POROSITY}} = {\left( \frac{W_{W} - {0.208\quad\left( W_{C} \right)}}{10} \right) + {\%\quad{AIR}}}$

Where,

W_(W)=weight of water per cubic meter of concrete,

W_(C)=weight of cement per cubic meter of concrete, and

% Air=percent volume of air in mixture based on volume of solids inmixture.

The above equation can thus be used with the slump and strength toinsure that a mixture has desired properties. That is, once a mixturehas been found to have sufficient strength and slump, the total porositycan be calculated to determine if it satisfies the desired porositylevel. If porosity is too high, the percent volume of cement can beincreased, thereby decreasing the porosity of the structure and ensuringthat it has sufficient durability.

L. Step 12: Optimizing Yield

Finally, step 12 involves determining the quantities of the variouscomponents of the optimal concrete mixture that are needed to produce adesired yield of a concrete composition. A detailed description of onecurrently preferred embodiment for accurately producing a desiredquantity of concrete from the optimal concrete mixture is set forth inthe Andersen patent at col. 45, line 63-col. 46, line 52. This sectionof Andersen et al. includes an exemplary mathematical algorithm relativeto determining raw materials quantities to ensure a desired yield andalso acts corresponding to step 12.

The volume of a proposed mixture is typically calculated by dividing theweight of each component by its respective density to obtain the volumeof each component. The volume of each of the components are then addedtogether to obtain the sum volume of the resulting mixture. Thisprocess, however, does not take into account that the packing density ofthe particles is less than 1.0 and, thus, does not consider theinterstitial spaces remaining between the mixed particles. As a result,the actual volume of the mixture is greater than the calculated volume.

The process for optimizing yield entails dividing the volume of eachcomponent (as determined by the previously discussed optimizationprocess) by the total volume of the mixture and then multiplying thecorresponding fractions by the desired volume of the mixture. Thesecalculations determine the actual volume of each component that shouldbe added to produce a mixture of a desired volume. In turn, the volumeof the components can be multiplied by their respective specificgravities to determine the weight of each component that should be addedto a mixture to obtain a desired yield of concrete.

By way of example, the volume of cement needed to produce 100 cubicmeters of a defined concrete mixture can be determined by the followingequation:Vol. Cement=(V _(C) /V _(T))·100

Where, V_(C)=the volume of cement in the mixture determined in Step 10of the optimization process and is represented as a fraction of thesolids in the mixture, the solids (i.e., cement, fine aggregate, coarseaggregate and, when relevant, fly ash and silica fume) summing to 1.0,

V_(T)=the total volume of the optimized mixture defined in Step 8, andis obtained by adding the volume of water, W, in the mixture to thevolume of solids (which sum to 1.0) and dividing the sum by the volumeof air in the mixture.

Hence, the total volume is represented by the following equation:$V_{T} = \frac{W + 1}{1 - \frac{\%\quad{AIR}}{100}}$

Where, the percent air, % Air, in the mixture can be empiricallydetermined by a trial mix. Using the above equation for each of thecomponents in the mixture, the volume of each of the components neededto produce a mixture with a desired yield can be accurately determined.

V. Computer-Implemented Iterative Design Optimization Sub-Routine orProcess

According to another aspect or embodiment of the present invention,there is provided a computer-implemented iterative optimization processaccording to the flow chart illustrated in FIG. 9, which may be utilizedalone or in combination with any part of the generalized processexemplified by Steps 1-12 described in Section IV. This process includesthe following steps:

-   -   1. providing batches of hydraulic cement and aggregate having        specific characteristics;    -   2. selecting a target slump and strength for the final concrete        composition;    -   3. measuring the average particle size and measuring or        estimating the packing density for the solid components        comprising hydraulic cement and each type of aggregate (e.g.,        fine, medium, and coarse aggregate);    -   4. designing a dry concrete mixture having a concentration ratio        of solid components;    -   5. calculating the particle packing density of the designed dry        concrete mixture;    -   6. calculating an amount of water that yields a designed        cementitious mixture having the target slump;    -   7. calculating the strength of the designed cementitious mixture        using Feret's equation, or a variant thereof, utilizing a        specific design K factor, from among different K factors that        lie along a K factor curve representative of system inputs, that        is selected based on the target strength (e.g., a specific        minimum desired or design compressive strength of the final        designed concrete mixture); calculating the difference between        the calculated strength of the designed cement mixture and the        target strength; and    -   9. altering the concentration ratio of the solid components to        yield one or more additional designed dry concrete mixtures and        then repeating steps 5 through 8 until the calculated strength        of one or more designed hydrated mixtures equals or is within an        acceptable range of deviation from the target strength.

The design K factor utilized in this process is ideally the same as thetheoretical or “true” K factor that corresponds to an ideal targetstrength. Nevertheless, the design K factor may deviate from thetheoretical K factor in order to guarantee a specific minimum concretestrength. The amount of deviation provides a margin of safety to accountfor variations between design strength and actual strength that mayoccur as a result of variations in raw materials characteristics and/orvariations in processing. Providing a better optimized mix designaccording to the invention significantly reduces the standard deviationbetween design strength and actual strength as compared to a poor,unoptimized mix design. Improvements and/or adjustments to processingequipment, as discussed elsewhere in this disclosure, can further reducethe deviation between design and actual strengths. Minimizing and/ormonitoring and accounting for changes in the raw materials can furtherreduce the deviation between design and actual strengths.

VI. Identifying Best Optimized Mix Design from Among Several DesignOptimized Hypothetical Mix Designs

FIG. 10 is a flow chat that illustrates an exemplary process accordingto the invention for designing several/hypothetical optimized mixdesigns and then identifying the best optimized mix design. The processillustrated in FIG. 10 demonstrates the use of a correct design K factorselected based on the desired or target strength. This process can beutilized using any desired computer-implemented design optimizationprocedure that utilizes Feret's equation or a variation thereof,including any processes disclosed herein. The design optimizationillustrated by FIG. 10 includes the following steps:

-   -   1. selecting the specific minimum desired or target strength for        a concrete composition;    -   2. selecting a design K factor based on the desired or target        strength, which may equal or deviate from theoretical K factor        that corresponds to that strength;    -   3. designing, using the design K factor, a plurality of        theoretically optimized concrete mix designs having a design        strength that is theoretically equal to the desired or target        strength;    -   4. preparing concrete test samples based on the theoretically        optimized concrete mix designs;    -   5. measuring the actual strengths of the concrete test samples;    -   6. comparing the difference between the actual strength for each        theoretically optimized mix design and the desired or target        strength; and    -   7. if the actual strength is not within an acceptable range of        deviation relative to the desired strength, designing one or        more additional concrete mix designs until the desired strength        of one or more additional concrete mix designs is within an        acceptable range of deviation from the desired strength.

The acceptable range of deviation between the actual strength and thedesired strength can be selected depending on the level of certaintydesired by the concrete manufacturer. An actual strength that is outsidethe acceptable range of deviation typically indicates a concrete mixturethat is overdesigned. Conversely, an actual strength that falls withinthe acceptable range of deviation is indicative of a better optimizedmix design.

VII. Manufacturing an Optimized Concrete Composition

FIG. 11 is a flow chart that illustrates an exemplary process formanufacturing an optimal concrete composition design using an inventivedesign optimization procedure set forth herein. The manufacturingprocess includes the following steps:

-   -   1. providing an optimal concrete mix design that was determined        using a design K factor that corresponds to a specific minimum        desired strength of the concrete to be manufactured;    -   2. determining a proper quantity for each solid component of the        concrete composition in order to provide an optimized yield that        guarantees a minimum required quantity while minimizing        overproduction and waste;    -   3. measuring the moisture content of the solid components used        to manufacture the concrete composition;    -   4. taking into account any moisture within the solid components,        weighing each solid component added to the concrete composition        to an accuracy of about ±2.0%, more preferably to an accuracy of        about ±1.0%, and most preferably to an accuracy of about 0.5%;    -   5. taking into account any moisture within the solid components,        determining an amount of batch water that, when blended with the        solid components, will yield a concrete composition having a        desired slump (e.g., according to the mix design); and    -   6. blending the components to yield a concrete composition in        which the actual strength and slump closely correlate to the        desired strength and slump.

According to one embodiment, it may be advantageous to control theconcentration of water from the time the concrete composition ismanufactured until the time it is delivered and used at the job site toprevent degradation of concrete strength. Additional information foroptimizing the mixing process and controlling water concentration willnow be given.

A. Controlling The Quantities of Components Added to Concrete

In order to obtain a concrete composition in which the actual strengthclosely corresponds to the desired or theoretical strength of theoptimized concrete mix design, it is preferable to carefully weight orotherwise measure the quantity of each component added to the concretecomposition. According to one embodiment, each component is preferablyweighed to an accuracy of about ±2.0%, more preferably to an accuracy ofabout ±1.0%, and most preferably to an accuracy of about ±0.5%. Anexample of apparatus that can be used to accurately weigh the variouscomponents added to a concrete delivery/mixer truck within the foregoingparameters is an Alkon Command Batch Weigh-up & Batching System. It willbe appreciated, however, that it is within the scope of the invention toutilize any other apparatus known in the art or that may be developedthat is capable of accurately weighing or otherwise measuring theamounts of the components added to the concrete mixer truck within thedesired level of accuracy.

B. Accounting for Variations in Moisture Content of Solid Components

According to one embodiment, it is advantageous to account forvariations in the moisture content of the solid components (i.e.,aggregates), which can significantly affect the strength and slump ofthe resulting concrete composition. Because moisture adds weight to theaggregates, failure to account and correct for this moisture can resultin using a lower quantity of one or more aggregates than what may berequired according to an optimized mix design. Providing a lesserquantity of one or more aggregates than what was determined by thedesign K factor to be optional can indirectly affect the strength of theresulting concrete composition (e.g., by increasing the amount of water,which increases the water-to-content ratio). In addition, reducing theamount of aggregates may increase the relative amount of hydrauliccement to beyond what was determined to be optimal. In addition toreducing strength, the unaccounted for excess water will also increasethe overall batch water content, which may increase slump to beyond whatwas determined to be optimal.

To account for moisture, sensors may be used to sense the moisturecontent of the solid components. Any moisture sensors known in the artor that may be developed can be used to monitor content. An example of amoisture sensor is a microwave sensor, which beams microwave radiationinto a given volume of material (e.g., fine, medium or coarse aggregate)and then measures the absorption of microwave energy by any water thatmay be present. Because water strongly absorbs microwave energy, the camount of microwave energy absorbed by a given volume of aggregatescorrelates with an amount of moisture within the aggregates. Theinformation regarding moisture content can be utilized to determine(e.g., by a computer) how much additional must be weighed out to providethe correct amount of aggregate and/or how much added water should beadded to the mixture to maintain the correct slump and/orwater-to-cement ratio. In general, smaller aggregates are more sensitiveto changes in moisture due to their generally higher surface area andability to absorb moisture into pores.

C. Use of Admixtures Instead of Water to Increase Slump

Equally or more important than controlling the initial quantities ofcomponents added to the concrete mixer/delivery truck is carefullycontrolling the concentration of batch water in the concrete compositionfrom between the time the components are added to the cement mixer drumto when the composition is delivered and utilized at the job site. Inorder to maintain a strength that meets or exceeds the specific minimumstrength, little or no additional water should ever be added to theconcrete composition once the components have been properly batched andmixed together.

In the event that it may be desired to alter the slump of the concretecomposition at a job site, only suitable chemical admixtures forincreasing or decreasing slump should be utilized. For example, where itis desired to increase the slump, one of the various plasticizers,super-plasticizers or high range water reducers known in the art can beutilized. Where it is desired to decrease slump, any of the knownrheology modifying agents or water binding agents known in the art canbe utilized. The quantity of such admixtures added to the concretecomposition should be carefully controlled in order to deliver aconcrete composition having the desired properties of slump andstrength.

D. Specially Designed Concrete Mixing Trucks

In current practice, slump modifications in concrete are typicallyperformed at the job site by the concrete truck driver adding additionalwater. This is the worst way to ensure desired strength since concretetruck drivers are typically the least knowledgeable regarding thedeleterious effect of adding water to concrete. In most cases, driversgo on look and feel rather than using a slump cone. This practice is socommon that concrete manufacturers are forced by necessity to overdesigntheir concrete mix designs by a significant margin.

In order to prevent a concrete truck driver from deliberately orinadvertently adding water to the concrete composition once it leavesthe concrete manufacturing site, it is within the scope of the inventionto utilize specially designed concrete mixing trucks that include a tankor vessel containing one or more admixtures used to make slumpadjustments as needed at the job site. For example, plasticizers,super-plasticizers or long-range water reducers known in the art can becontained within one or more vessels. In addition, the concrete mixingtruck may include a device that accurately measures the slump of theconcrete mixture within the drum. If it is necessary or desired toincrease the slump of the concrete mixture, a pre-determined quantity ofthe slump increasing admixture can be injected from the special tank orvessel into the drum in order to raise the slump to the desired value.

A separate vessel or tank may also include admixtures that are capableof altering the concrete composition in other ways (e.g., increasingcohesion, decreasing slump, increasing set time, or retarding set time).Because such admixtures do not typically affect strength, the desiredminimum strength can more easily be maintained, thereby furtherdecreasing the deviation between actual and design strength (and actualand design K factor).

Concrete delivery trucks are typically equipped with water tanks to addwater on site. Some are also equipped with admixture tanks to meteradmixtures. One of skill in the art, knowing how admixtures affectslump, can readily design a concrete truck that is able to meter aspecific quantity of slump altering admixture as may be needed todesired to alter slump in the appropriate manner. Thus, only minormodifications of existing concrete trucks may be required. Suchapparatus comprising means for metering a desired quantity of admixtureto a concrete composition on site.

E. Abbreviated Re-Design Process to Adjust Slump of an Optimized MixDesign Without Substantially Altering Compressive Strength

In some cases it may be desirable to quickly re-design a mix design thatis already optimized in order to adjust the slump without significantlychanging the compressive strength. This can be done without creating awhole new optimized mix design using, e.g., the detailed 12-step designoptimization procedure described above. To maintain the same essentialstrength, while varying the slump, the same water-to-cement ratio of thepaste is maintained. Only the volume of paste is altered in order toadjust the slump of the wet cementitious mixture. In general, addingmore paste will increase slump, while adding less paste will decreasethe slump. Thus, the overall ratio of cement paste to aggregate isadjusted to change the slump. Because the water-to-cement ratio of thepaste remains the same, the strength will theoretically remainessentially the same. In some cases, the ratio of fine to coarseaggregates may remain the same. In other cases, the ratio can be alteredsomewhat depending on the effect on the other properties caused bychanging the overall ratio of cement paste to aggregate (e.g.,cohesiveness, durability, and the like).

A flow chart illustrating an exemplary method for the abbreviatedre-design of a current optimized mix design in order to adjust slump isshown in FIG. 12. The effect of changing the overall concentration ofcement paste on slump can be determined using any of the slump equationsset forth above and accounting for the increased or decreased watercontent depending on whether the amount of cement paste is increased ordecreased compared to the initial mix design. Adding more cement pasteincreases slump because it increases the overall concentration ofwater-to-solid components. Conversely, decreasing the quantity of cementpaste decreases slump because it decreases the overall ration ofwater-to-solid components.

According to one embodiment, the process is controlled by a computer andinvolves monitoring changes in slump between batches, which might becaused by variations in aggregate size and/or moisture. When a change inslump is detected, a computer-implemented design process involvesadjusting the quantity of water in order to revise the slump, changingthe amount of cement to maintain the same water to cement ratio (andtherefore strength), and altering the relative concentration ofaggregates if needed to maintain a proper amount of cohesiveness. Ingeneral, increasing the ratio of fine aggregate to coarse aggregateincreases cohesiveness but can decrease slump. A decrease in cementpaste may require an increase in fine aggregate to maintaincohesiveness. Conversely, an increase in cement paste may require adecrease in fine aggregate to increase slump while avoiding thedeleterious effect of overcementing and in order to better optimizecost.

In some cases, it may be possible to select a ratio of fine to coarseaggregate that is not necessarily perfectly optimized but that isadequate (e.g., typically within a range of 40:60 to 60:40 parts fine tocoarse aggregate). Within this ratio there is often not a lot ofvariability in cohesion and segregation, which can greatly affectconcrete performance when placed at a job site. To ensure a minimumguaranteed strength, a cement paste is designed having a water to cementratio that yield the desired strength (e.g., in the case where thecement paste is the weakest component). The ratio of cement paste toaggregate is adjusted to yield the desired slump. While this approachdoes not optimize concrete to the same degree of accuracy, it can beemployed in many cases (e.g., smaller jobs where the relatively smallcost of overdesigning may not justify a full-blown optimizationprocedure as described herein).

VIII. Redesigning a Pre-Existing Concrete Mix Design

FIG. 13 is a flow chart that illustrates an exemplary method forredesigning a pre-existing concrete mix design utilizing the recentlydiscovered knowledge that and how the K factor used in Feret's equationvaries with changes in concrete strength (i.e., logarithmically withincreasing strength). The exemplary redesign process shown in FIG. 13includes the following steps:

-   -   1. identifying a pre-existing concrete mix design having a        predicted (or design) strength;    -   2. preparing a concrete test sample from the pre-existing        concrete mix design;    -   3. measuring the actual strength of the concrete test sample and        determining how much the actual strength deviates from the        design strength (optional);    -   4. determining an apparent design K factor for the pre-existing        concrete mix design based on the design strength and the ratio        of components OZ within the concrete test sample made from the        pre-existing concrete mix design;    -   5. comparing the apparent design K factor of the pre-existing        concrete mix design with the “true” or optimal K factor        corresponding to the design or predicted strength of the        pre-existing concrete mix design;    -   6. identifying a revised design K factor based on the predicted        (or design) strength (e.g., selected based on one of the K        factor lines shown in FIGS. 1-3 or that is appropriate for the        given set of raw material inputs) that is closer to the optimal        K factor for the design strength than the apparent design K        factor of the pre-existing mix design; a K factor curve for the        concrete plant can be optionally constructed by testing the        actual strength of one or more properly prepared concrete        compositions of the manufacturer and plotting the actual K        factor(s) versus actual strength; and    -   7. designing, using the revised design K factor, a new concrete        mix design that yields a concrete composition having an actual        strength that more consistently corresponds to the predicted (or        design) strength compared to the pre-existing mix design.

In the case of an unoptimized, poorly pre-existing mix design, thedifference between the apparent design K factor based on the design orpredicted strength of the pre-existing mix design and the optimal ortheoretical K factor based on the design strength will be significantlygreater than in an optimized mix design. By rebalancing the relativeconcentrations of the various components in order to yield a moreoptimized mix design (i.e., so as to more efficiently utilize thehydraulic cement and other components), the deviation between actualstrength and design strength will be significantly decreased. As aresult, the revised design K factor that is required to guarantee aspecific minimum strength will more closely correspond to the optimal ortheoretical K factor compared to the pre-existing, unoptimized mixdesign. Moreover, comparing the difference between the apparent design Kfactor and the optimal K factor is a diagnostic tool that enables onedesiring to implement the design optimization procedure of the presentinvention to diagnose if, and to what extent, a pre-existing mix designmay be overdesigned. As discussed elsewhere, the deviation between thedesign and optimal K factors can be achieved by carefully accounting forvariations in the size and moisture content of the solid componentsand/or upgrading and/or adjusting the manufacturing process andequipment.

IX. Upgrading an Existing Concrete Plant

FIG. 14 is a flow chart that illustrates an exemplary embodimentaccording to the invention for upgrading an existing concretemanufacturing plant. The process illustrated in FIG. 14 utilizes thediscovery that and how the K factor various logarithmically with changesin concrete strength. The process for upgrading an existing concretemanufacturing plant includes the following steps:

-   -   1. manufacturing one or more concrete compositions using one or        more pre-existing mix designs having predicted strengths;    -   2. determining an apparent design K factor for each of the one        or more concrete compositions based on the design strength and        ratio of components of each concrete composition;    -   3. identifying a revised design K factor, based on the predicted        or desired strength of each pre-existing mix design, which more        closely corresponding to the optimal or true K factor for the        design strength compared to the pre-existing mix design; and    -   4. designing, using the revised design K factor for each        pre-existing mix design, one or more revised concrete mix        designs that yield concrete compositions having actual strengths        that more consistently correspond to the predicted or design        strengths compared to the one or more pre-existing mix designs,        respectively.

Because each manufacturing plant has its own unique set of raw materialsand/or processing inputs (i.e., no two plants use exactly the same rawmaterials and possess the exact same equipment calibrated and/oroperated in the exact same manner), it will be appreciated that eachmanufacturing plant produces concrete compositions having unique aspectsthat are specific to a given manufacturing plant. In other words, evenif two manufacturing plants use the same standardized mix designs (i.e.,recipes), the concrete delivered by each plant will, in same way, beunique to each plant. That means that pre-existing concrete mix designsthat have been modified and optimized utilizing the improved DOC programwill yield new concrete compositions that are themselves unique in thatthey will have never been manufactured at any time anywhere in theworld. Thus, improved concrete compositions manufactured using optimizedmix designs resulting from the implementation of the improved DOCprocess are themselves unique and therefore novel as between allpreviously manufactured concrete.

It turns out that every concrete composition that is made has its ownunique signature design K factor and also an actual K factor that can bedetermined by testing the actual strength of the composition. That istrue both before and after implementation of the improved DOC process.However, after implementation of the improved DOC process, the signatureK factors, both design and actual, for an optimized concrete compositionof a manufacturing plant will exceed the signature K it, factors, bothdesign and actual, of the pre-existing concrete composition that wasredesigned using the improved DOC process. By knowing and comparing thedesign and/or signature K factors of both a pre-existing and anoptimized concrete composition of a given manufacturing plant, one canreadily ascertain whether a particular concrete composition produced bythe manufacturing plant was manufactured using the pre-existing mixdesign or an optimized mix design designed using the improved DOCprocess. Thus, the signature K factor can be used as a diagnostic toolto distinguish whether an overdesigned or an optimized concretecomposition was used in a building project (i.e., to determine whetheror not the improved DOC process has been implemented by a concretemanufacturer in designing its concrete compositions).

One of the practical affects of upgrading an existing concretemanufacturing plant is providing mix designs that are specificallyoptimized based on the raw materials that are actually used by theconcrete manufacturing plant. It is often the case that manufacturingplants use standardized mix designs that were made using raw materialsnot available to a particular manufacturing plant. Indeed, manufacturingplants are often owned by a single entity that provides standardized mixdesigns for use with every manufacturing plant regardless of variationsin raw material inputs. As a result, there is large systematic errorbuilt into the standardized mix designs that cannot be accounted for orcorrected by simply providing improved batching equipment. In otherwords, even if the components could be measured and batched perfectlyeach time, the mix designs would have to account for variations in rawmaterials inputs among and between the various manufacturing plants. Theonly way to eliminate such systematic error is to provide an optimizedmix design that is specifically tailored to account for the specific rawmaterials that are used by a particular manufacturing plant to makeconcrete at a given time.

The knowledge of how the K factor varies with concrete strength can beused as a diagnostic tool to identify those aspects of a manufacturer'sbatching process that may be in need of modification. As discussedherein, the improved DOC process can be used to identify how much pasteis needed to achieve a desired slump, with the K factor specifying thewater-to-cement ratio needed to obtain a specific strength. If particlepacking is optimized for a particular plant, there is little benefit inspending capital resources to optimize the metering equipment.Increasing the ability to accurately weigh and batch solid componentswill not yield much benefit if particle packing is already optimized ornearly optimized. If variations in weighing the aggregates does notappreciatively affect slump, then it will also not appreciatively affectstrength even if the aggregates are not weighed to a high degree ofaccuracy.

On the other hand, where much more cement paste is required to achieve adesired slump compared to an optimized particle packing system, thatindicates that much more accurately weighing the aggregates to achieveoptimized particle packing will yield significant benefits. In otherwords, if more accurately measuring the fine and coarse aggregatesminimizes or eliminates changes in slump and also reduces or eliminatesovercementing required to achieve desired slump, investment in moreaccurate weighing apparatus would be highly beneficial and worth thecost.

In addition to accurately weighing the various components added to abatch of concrete, accounting for variations in moisture content of theaggregates will also yield large benefits in the case where moisturevariation is a problem. Variations in moisture not only affect how muchaggregate is needed but also greatly affect how much water is containedin the concrete composition, thereby affecting water-to-cement ratio andslump to a high degree. Accounting for all water inputs greatlyincreases the ability to consistently provide concrete having thedesired slump and strength such that a capital investment in moisturesensing material may be justified.

X. Examples of Design Optimization Process to Re-Design Or ReplacePre-Existing Mix Designs

The following examples demonstrate the ability of the improved DOCprocess disclosed herein to modify, redesign and/or replace pre-existingmix designs currently used in the industry in order to yield improvedconcrete mixtures that are better optimized with respect to cost, whilealso maintaining the desired properties (e.g., slump and strength). Thesame procedures can also be carried out relative to virtually any knownmix designed currently known and used in the concrete industry in orderto optimize such compositions with respect to strength and cost, whilealso maintaining other desired properties.

The inventive design optimization methods were used to improve mixdesigns at various concrete manufacturing plants throughout the UnitedStates, demonstrating the universal applicability of the inventivemethods. Examples 1-4 relate to four optimized concrete mix designs thatwere made according to the improved DOC process to improve upon andreplace 12 standard mix designs presently or previously used by a firstmanufacturing plant using standardized mix designs. The standard mixdesigns in the remaining comparative examples are the same as inExamples 1-4, but were used by other plants owned by the samemanufacturer. For this reason, the cost of manufacturing concrete at thedifferent plants differs due to differences in the raw materials costdue to location and source. Because the quality of aggregates differfrom plant to plant, the design optimization procedure yields differentoptimized mix designs for each manufacturing plant in order to accountfor such differences in raw material inputs. In this way, the optimizedmix designs are better tailored to the specific raw materials used byeach plant.

The standard pre-existing mix designs are “comparative examples” andshall be numbered according to the corresponding optimized mix designcreated to take their place (e.g., the optimized mix design of Example 1corresponds to, and is designed to replace, the mix designs ofComparative Examples 1a-1c).

Examples 1-4

Examples 1-4 illustrate four optimized concrete mix designs that wereprepared using the improved DOC process described herein. The four mixdesigns of Examples 1-4 can replace twelve pre-existing standardconcrete mix designs utilized by an existing concrete manufacturingplant. Each mix design of Examples 1-4 corresponds to a group of threepre-existing mix designs of similar type that guarantee a minimumcompressive strength, at a specified slump, and percentage of entrainedair when delivered to the customer. The pre-existing mix designs of theconcrete manufacturing plant, their components, cost (revised Apr. 7,2006), and apparent design K factors, will be presented in four groupsof three concrete mix designs, each group having similar properties orcharacteristics.

Comparative Examples 1a-1c

The three mix designs of Comparative Examples 1a-1c have a designstrength of 3000 psi, a slump of 4 inches, and minimal entrained air(1.5%). Comparative Example 1a 1b 1c Cost (US$) Compressive Strength3000 3000 3000 — (psi) Slump (inch) 4 4 4 — Type 1 Cement 370 470 423$101.08/Ton (lbs/yd³) Type C Fly Ash 100 0 0 $51.00/Ton (lbs/yd³) Sand(lbs/yd³) 1570 1470 1660 $9.10/Ton State Rock (lbs/yd³) 1700 1700 1714$11.65/Ton Potable Water 280 280 265 negligible (lbs/yd³) Daravair 1400(air 0 0 0 $3.75/Gal entrain.) (fl. oz./cwt) Daracem 65 (water 0 0 14.8$5.65/Gal red.) (fl. oz./cwt) % Air 1.5 1.5 1.5 — Apparent Design K 234191 207 — Factor Cost ($/yd³) $38.59 $40.62 $41.99 — Sales Distribution(%) 19.57 80.43 0 — Within Group Weighted Average $40.23 — Cost ($/yd³)Total Sales (%) of 1.08 — Concrete Plant

Comparative Examples 2a-2c

The three mix designs of Comparative Examples 2a-2c have a designstrength of 3000 psi, a slump of 4 inches, and substantial entrained air(5%). Comparative Example 2a 2b 2c Cost (US$) Compressive Strength 30003000 3000 — (psi) Slump (inch) 4 4 4 — Type 1 Cement 350 470 423$101.08/Ton (lbs/yd³) Type C Fly Ash 100 0 0 $51.00/Ton (lbs/yd³) Sand(lbs/yd³) 1510 1420 1560 $9.10/Ton State Rock (lbs/yd³) 1750 1750 1740$11.65/Ton Potable Water 250 260 240 negligible (lbs/yd³) Daravair 1400(air 4 5 4 $3.75/Gal entrain.) (fl. oz./cwt) Daracem 65 (water 0 0 14.8$5.65/Gal red.) (fl. oz./cwt) % Air 5 5 5 — Apparent Design K 237 189199 — Factor Cost ($/yd³) $38.00 $41.37 $42.37 — Sales Distribution (%)74.23 25.77 0 — Within Group Weighted Average $38.87 — Cost ($/yd³)Total Sales (%) of 17.53 — Concrete Plant

Comparative Examples 3a-3c

The three mix designs of Comparative Examples 3a-3c have a designstrength of 4000 psi, a slump of 4 inches, and minimal entrained air(1.5%). Comparative Example 3a 3b 3c Cost (US$) Compressive Strength4000 4000 4000 — (psi) Slump (inch) 4 4 4 — Type 1 Cement 470 564 517$101.08/Ton (lbs/yd³) Type C Fly Ash 100 0 0 $51.00/Ton (lbs/yd³) Sand(lbs/yd³) 1530 1440 1530 $9.10/Ton State Rock (lbs/yd³) 1746 1750 1750$11.65/Ton Potable Water 280 285 280 negligible (lbs/yd³) Daravair 1400(air 0 0 0 $3.75/Gal entrain.) (fl. oz./cwt) Daracem 65 (water 0 0 18.1$5.65/Gal red.) (fl. oz./cwt) % Air 1.5 1.5 1.5 — Apparent Design K 232206 226 — Factor Cost ($/yd³) $43.73 $45.53 $47.71 — Sales Distribution(%) 6.81 44.35 48.84 — Within Group Weighted Average $46.47 — Cost($/yd³) Total Sales (%) of 12.81 — Concrete Plant

Comparative Examples 4a-4c

The three mix designs of Comparative Examples 4a-4c have a designstrength of 4000 psi, a slump of 4 inches, and substantial entrained air(5%). Comparative Example 4a 4b 4c Cost (US$) Compressive Strength 40004000 4000 — (psi) Slump (inch) 4 4 4 — Type 1 Cement 470 564 517$101.08/Ton (lbs/yd³) Type C Fly Ash 100 0 0 $51.00/Ton (lbs/yd³) Sand(lbs/yd³) 1390 1340 1430 $9.10/Ton State Rock (lbs/yd³) 1710 1750 1750$11.65/Ton Potable Water 255 275 255 negligible (lbs/yd³) Daravair 1400(air 4 5 4 $3.75/Gal entrain.) (fl. oz./cwt) Daracem 65 (water 0 0 18.1$5.65/Gal red.) (fl. oz./cwt) % Air 5 5 5 — Apparent Design K 224 212218 — Factor Cost ($/yd³) $43.41 $45.88 $47.99 — Sales Distribution (%)77.31 22.69 0 — Within Group Weighted Average $43.97 — Cost ($/yd³)Total Sales (%) of 68.58 — Concrete Plant

The following optimized concrete mix designs according to Examples 1-4were made according to the improved DOC process and are intended toreplace the 12 mix designs of Comparative Examples 1a-4c. Each optimizedmix design takes the place of three mix designs of similar attributes(e.g., the optimized mix design of Example 1 takes the place of thepre-existing mix designs of Comparative Examples 1a-1c). Theoptimization procedure assumed a percent absorption for the sand androck of 1.5% and 2.5%, respectively, and a percent moisture of 4.57% and3.18%, respectively. Example 1 2 3 4 Cost (US$) Compressive 3000 30004000 4000 — Strength (psi) Slump (inch) 5 5 5 5 — Type 1 Cement 340 299375 366 $101.08/Ton (lbs/yd³) Type C Fly Ash 102 90 113 110 $51.00/Ton(lbs/yd³) Sand (lbs/yd³) 1757 1697 1735 1654 $9.10/Ton State Rock(lbs/yd³) 1452 1403 1434 1367 $11.65/Ton Potable Water 294 269 294 269negligible (lbs/yd³) Daravair 1400 (air 0 1.4 0 1.4 $3.75/Gal entrain.)(fl. oz./cwt) % Air 2 5.5 2 5.5 $5.65/Gal Cost ($/yd³) $36.55 $33.72$38.39 $37.23 — Weighted Avg. Cost $36.76 — ($/yd³) Cost Savings ($/yd³)$3.68 $5.15 $8.08 $6.74 — Per Mix Design Weighted Avg. $6.60 — PlantCost Savings ($/yd³)

Many concrete manufacturing plants have an excessive number of mixdesigns of similar type in an attempt to satisfy customer need. Eachimproved mix design of Examples 1-4 is able to take the place of threepre-existing standard mix designs of similar type because it satisfiesthe criteria of all three mix designs while also having reduced cost.Reducing the number of mix designs required to satisfy customer needrepresents an additional cost savings to a concrete manufacturing plantbecause it simplifies the overall manufacturing process.

The absolute cost savings ranged from a low of $2.04 per yard (Example 1relative to Comparative Example 1a) to a high of $10.76 per yard(Example 4 relative to Comparative Example 4c). The weighted averagecost of the pre-existing mix designs of Comparative Examples 1a-4c,based on the percentage of each mix design sold by the manufacturingplant, is $43.36 per yard (as of Apr. 7, 2006). The weighted averagecost to manufacture concrete using the four optimized mix designs basedon existing sales percentages for the 12 pre-existing mix designs of themanufacturer would be $36.76 per yard at the same materials cost percomponent. The average overall cost savings for the manufacturing plantwould therefore be $6.60 per yard, assuming the manufacturer were toreplace the 12 pre-existing mix designs of Comparative Examples with theoptimized mix designs of Examples 1-4 and continue to manufacture thesame distribution of concrete as before.

The amount of $6.60 is several times greater than the typical profit of$1-2 per yard earned by typical concrete manufacturers after all fixedand variable costs of operating the manufacturing plant are factored inand accounted for. The improved design optimization procedures aretherefore able to dramatically improve upon pre-existing mix designsused by manufacturers, which were thought to be optimal based on decadesof testing and use, and increase profits by several times. This is asurprising and unexpected result that attests to the contribution to theart of concrete manufacture provided by the improved DOC process of thepresent invention. Whereas the original DOC program of the Andersenpatent had much to commend itself, it could not be readily implementedin the real world to diagnose and improve upon pre-existing concrete mixdesigns in a concrete and verifiable manner in order to yielddemonstrably improved results at reduced cost. The improvementsdescribed herein were necessary to provide an optimization procedurethat could be readily implemented as illustrated in Examples 1-4.

Examples 5-8

Examples 5-8 illustrate four optimized concrete mix designs that wereprepared using the improved DOC process described herein. The four mixdesigns of Examples 5-8 can replace twelve pre-existing standardconcrete mix designs of an existing concrete manufacturing plant, whichused the same 12 mix designs as in Comparative Examples 1a-4c butmanufactured concrete using a different set of raw materials. Each mixdesign of Examples 5-8 corresponds to a group of three pre-existing mixdesigns of similar type that guarantee a minimum compressive strength,at a specified slump, and percentage of entrained air when delivered tothe customer. The pre-existing mix designs of the concrete manufacturingplant, their components, cost (revised Oct. 27, 2005), and apparentdesign K factors, will be presented in four groups of three concrete mixdesigns, each group having similar properties or characteristics.

Comparative Examples 5a-5c

The three mix designs of Comparative Examples 5a-5c have a designstrength of 3000 psi, a slump of 4 inches, and minimal entrained air(1.5%). Comparative Example 5a 5b 5c Cost (US$) Compressive Strength3000 3000 3000 — (psi) Slump (inch) 4 4 4 — Type 1 Cement 370 470 423$104/Ton (lbs/yd³) Type C Fly Ash 100 0 0 $47.00/Ton (lbs/yd³) Sand(lbs/yd³) 1570 1470 1660 $4.46/Ton ¾ inch Rock (lbs/yd³) 1700 1700 1714$4.46/Ton Potable Water 280 280 265 Negligible (lbs/yd³) Daravair (airentrain.) 0 0 0 $3.75/Gal (fl. oz./cwt) Daracem (water red.) 0 0 14.8$5.65/Gal (fl. oz./cwt) % Air 1.5 1.5 1.5 — Apparent Design K 234 191207 — Factor Cost ($/yd³) $29.01 $31.63 $32.42 — Sales Distribution (%)19.57 80.43 0 — Within Group Weighted Average $31.12 — Cost ($/yd³)Total Sales (%) of 1.08 — Concrete Plant

Comparative Examples 6a-6c

The three mix designs of Comparative Examples 6a-6c have a designstrength of 3000 psi, a slump of 4 inches, and substantial entrained air(5%). Comparative Example 6a 6b 6c Cost (US$) Compressive Strength 30003000 3000 — (psi) Slump (inch) 4 4 4 — Type 1 Cement 350 470 423$104/Ton (lbs/yd³) Type C Fly Ash 100 0 0 $47.00/Ton (lbs/yd³) Sand(lbs/yd³) 1510 1420 1560 $4.46/Ton ¾ inch Rock (lbs/yd³) 1750 1750 1740$4.46/Ton Potable Water 250 260 240 negligible (lbs/yd³) Daravair (airentrain.) 4 5 4 $3.75/Gal (fl. oz./cwt) Daracem (water red.) 0 0 14.8$5.65/Gal (fl. oz./cwt) % Air 5 5 5 — Apparent Design K 237 189 199 —Factor Cost ($/yd³) $28.36 $32.32 $32.74 — Sales Distribution (%) 74.2325.77 0 — Within Group Weighted Average $29.38 — Cost ($/yd³) TotalSales (%) of 17.53 — Concrete Plant

Comparative Examples 7a-7c

The three mix designs of Comparative Examples 7a-7c have a designstrength of 4000 psi, a slump of 4 inches, and minimal entrained air(1.5%). Comparative Example 7a 7b 7c Cost (US$) Compressive Strength4000 4000 4000 — (psi) Slump (inch) 4 4 4 — Type 1 Cement 470 564 517$104/Ton (lbs/yd³) Type C Fly Ash 100 0 0 $47.00/Ton (lbs/yd³) Sand(lbs/yd³) 1530 1440 1530 $4.46/Ton ¾ inch Rock (lbs/yd³) 1746 1750 1750$4.46/Ton Potable Water 280 285 280 negligible (lbs/yd³) Daravair (airentrain.) 0 0 0 $3.75/Gal (fl. oz./cwt) Daracem (water red.) 0 0 18.1$5.65/Gal (fl. oz./cwt) % Air 1.5 1.5 1.5 — Apparent Design K 232 206226 — Factor Cost ($/yd³) $34.22 $36.56 $38.46 — Sales Distribution (%)6.81 44.35 48.84 — Within Group Weighted Average $37.33 — Cost ($/yd³)Total Sales (%) of 12.81 — Concrete Plant

Comparative Examples 8a-8c

The three mix designs of Comparative Examples 8a-8c have a designstrength of 4000 psi, a slump of 4 inches, and substantial entrained air(5%). Comparative Example 8a 8b 8c Cost (US$) Compressive Strength 40004000 4000 — (psi) Slump (inch) 4 4 4 — Type 1 Cement 470 564 517$104/Ton (lbs/yd³) Type C Fly Ash 100 0 0 $47.00/Ton (lbs/yd³) Sand(lbs/yd³) 1390 1340 1430 $4.46/Ton ¾ inch Rock (lbs/yd³) 1710 1750 1750$4.46/Ton Potable Water 255 275 255 negligible (lbs/yd³) Daravair (airentrain.) 4 5 4 $3.75/Gal (fl. oz./cwt) Daracem (water red.) 0 0 18.1$5.65/Gal (fl. oz./cwt) % Air 5 5 5 — Apparent Design K 224 212 218 —Factor Cost ($/yd³) $34.37 $37.16 $38.99 — Sales Distribution (%) 77.3122.69 0 — Within Group Weighted Average $35.01 — Cost ($/yd³) TotalSales (%) of 68.58 — Concrete Plant

The following optimized concrete mix designs according to Examples 5-8were made according to the improved DOC process and are intended toreplace the 12 mix designs of Comparative Examples 5a-8c. Each optimizedmix design takes the place of three mix designs of similar attributes(e.g., the optimized mix design of Example 5 takes the place of thepre-existing mix designs of Comparative Examples 5a-5c). Theoptimization procedure assumed a percent absorption for the sand androck of 1.9% and 2.3%, respectively, and a percent moisture of 4.57% and3.18%, respectively. Example 5 6 7 8 Cost (US$) Compressive 3000 30004000 4000 — Strength (psi) Slump (inch) 5 5 5 5 — Type 1 Cement 332 302375 366 $104/Ton (lbs/yd³) Type C Fly Ash 100 91 112 110 $47.00/Ton(lbs/yd³) Sand (lbs/yd³) 1769 1693 1737 1657 $4.46/Ton ¾ inch Rock 14701407 1450 1377 $4.46/Ton (lbs/yd³) Potable Water 294 274 295 270negligible (lbs/yd³) Daravair 0 1.4 0 1.4 $3.75/Gal (fl. oz./cwt) % Air1.8 5.5 1.9 5.4 $5.65/Gal Cost ($/yd³) $26.97 $25.01 $29.37 $28.66 —Weighted Avg. Cost $28.09 — ($/yd³) Cost Savings ($/yd³) $4.15 $4.37$7.96 $6.34 — Per Mix Design Weighted Avg. $6.18 — Plant Cost Savings($/yd³)

Each improved mix design of Examples 5-8 is able to take the place ofthree pre-existing standard mix designs of similar type because itsatisfies the criteria of all three mix designs while also havingreduced cost. The reduced number of mix designs is an additional costsavings as it simplifies the overall manufacturing process.

The absolute cost savings ranged from a low of $2.04 per yard (Example 5relative to Comparative Example 5a) to a high of $10.32 per yard(Example 8 relative to Comparative Example 8c). The weighted averagecost of the pre-existing mix designs of Comparative Examples 5a-8c,based on the percentage of each mix design sold by the manufacturingplant, is $34.27 per yard (as of Oct. 27, 2005). The weighted averagecost to manufacture concrete using the four optimized mix designs basedon existing sales percentages for the 12 pre-existing mix designs of themanufacturer would be $28.09 per yard at the same materials cost percomponent. The average overall cost savings for the manufacturing plantwould therefore be $6.18 per yard, assuming the manufacturer were toreplace the 12 pre-existing mix designs of Comparative Examples 5a-8cwith the optimized mix designs of Examples 5-8 and continue tomanufacture the same distribution of concrete as before.

Examples 9-12

Examples 9-12 illustrate four optimized concrete mix designs that wereprepared using the improved DOC process described herein. The four mixdesigns of Examples 9-12 can replace twelve pre-existing standardconcrete mix designs of an existing concrete manufacturing plant, whichused the same 12 mix designs as in Comparative Example 1a-4c butmanufactured concrete using a different set of raw materials. Each mixdesign of Examples 9-12 corresponds to a group of three pre-existing mixdesigns of similar type that guarantee a minimum compressive strength,at a specified slump, and percentage of entrained air when delivered tothe customer. The pre-existing mix designs of the concrete manufacturingplant, their components, cost (revised Oct. 27, 2005), and apparentdesign K factors, will be presented in four groups of three concrete mixdesigns, each group having similar properties or characteristics.

Comparative Examples 9a-9c

The three mix designs of Comparative Examples 9a-9c have a designstrength of 3000 psi, a slump of 4 inches, and minimal entrained air(1.5%). Comparative Example 9a 9b 9c Cost (US$) Compressive Strength3000 3000 3000 — (psi) Slump (inch) 4 4 4 — Type 1 Cement 370 470 423$104/Ton (lbs/yd³) Type C Fly Ash 100 0 0 $47.00/Ton (lbs/yd³) Sand(lbs/yd³) 1570 1470 1660 $8.12/Ton 1 inch Rock (lbs/yd³) 1700 1700 1714$9.36/Ton Potable Water 280 280 265 Negligible (lbs/yd³) Daravair (airentrain.) 0 0 0 $3.75/Gal (fl. oz./cwt) Daracem (water red.) 0 0 14.8$5.65/Gal (fl. oz./cwt) % Air 1.5 1.5 1.5 — Apparent Design K 234 191207 — Factor Cost ($/yd³) $36.21 $38.64 $39.82 — Sales Distribution (%)19.57 80.43 0 — Within Group Weighted Average $38.16 — Cost ($/yd³)Total Sales (%) of 1.08 — Concrete Plant

Comparative Examples 10a-10c

The three mix designs of Comparative Examples 10a-10c have a designstrength of 3000 psi, a slump of 4 inches, and substantial entrained air(5%). Comparative Example 10a 10b 10c Cost (US$) Compressive Strength3000 3000 3000 — (psi) Slump (inch) 4 4 4 — Type 1 Cement 350 470 423$104/Ton (lbs/yd³) Type C Fly Ash 100 0 0 $47.00/Ton (lbs/yd³) Sand(lbs/yd³) 1510 1420 1560 $8.12/Ton 1 inch Rock (lbs/yd³) 1750 1750 1740$9.36/Ton Potable Water 250 260 240 negligible (lbs/yd³) Daravair (airentrain.) 4 5 4 $3.75/Gal (fl. oz./cwt) Daracem (water red.) 0 0 14.8$5.65/Gal (fl. oz./cwt) % Air 5 5 5 — Apparent Design K 237 189 199 —Factor Cost ($/yd³) $35.56 $39.36 $40.02 — Sales Distribution (%) 74.2325.77 0 — Within Group Weighted Average $36.54 — Cost ($/yd³) TotalSales (%) of 17.53 — Concrete Plant

Comparative Examples 11a-11c

The three mix designs of Comparative Examples 11a-11c have a designstrength of 4000 psi, a slump of 4 inches, and minimal entrained air(1.5%). Comparative Example 11a 11b 11c Cost (US$) Compressive Strength4000 4000 4000 — (psi) Slump (inch) 4 4 4 — Type 1 Cement 470 564 517$104/Ton (lbs/yd³) Type C Fly Ash 100 0 0 $47.00/Ton (lbs/yd³) Sand(lbs/yd³) 1530 1440 1530 $8.12/Ton 1 inch Rock (lbs/yd³) 1746 1750 1750$9.36/Ton Potable Water (lbs/yd³) 280 285 280 negligible Daravair (airentrain.) 0 0 0 $3.75/Gal (fl. oz./cwt) Daracem (water red.) 0 0 18.1$5.65/Gal (fl. oz./cwt) % Air 1.5 1.5 1.5 — Apparent Design K 232 206226 — Factor Cost ($/yd³) $41.46 $43.64 $45.70 — Sales Distribution (%)6.81 44.35 48.84 — Within Group Weighted Average $44.50 — Cost ($/yd³)Total Sales (%) of 12.81 — Concrete Plant

Comparative Examples 12a-12c

The three mix designs of Comparative Examples 12a-12c have a designstrength of 4000 psi, a slump of 4 inches, and substantial entrained air(5%). Comparative Example 12a 12b 12c Cost (US$) Compressive Strength4000 4000 4000 — (psi) Slump (inch) 4 4 4 — Type 1 Cement 470 564 517$104/Ton (lbs/yd³) Type C Fly Ash 100 0 0 $47.00/Ton (lbs/yd³) Sand(lbs/yd³) 1390 1340 1430 $8.12/Ton 1 inch Rock (lbs/yd³) 1710 1750 1750$9.36/Ton Potable Water (lbs/yd³) 255 275 255 negligible Daravair (airentrain.) 4 5 4 $3.75/Gal (fl. oz./cwt) Daracem (water red.) 0 0 18.1$5.65/Gal (fl. oz./cwt) % Air 5 5 5 — Apparent Design K 224 212 218 —Factor Cost ($/yd³) $41.25 $44.05 $46.04 — Sales Distribution (%) 77.3122.69 0 — Within Group Weighted Average $41.89 — Cost ($/yd³) TotalSales (%) of 68.58 — Concrete Plant

The following optimized concrete mix designs according to Examples 9-12were made according to the improved DOC process and are intended toreplace the 12 mix designs of Comparative Examples 9a-12c. Eachoptimized mix design takes the place of three mix designs of similarattributes (e.g., the optimized mix design of Example 9 takes the placeof the pre-existing mix designs of Comparative Examples 9a-9c). Theoptimization procedure assumed a percent absorption for the sand androck of 1.9% and 1.8%, respectively, and a percent moisture of 4.57% and3.18%, respectively. Example 9 10 11 12 Cost (US$) Compressive 3000 30004000 4000 — Strength (psi) Slump (inch) 5 5 5 5 — Type 1 Cement 336 293376 362 $104/Ton (lbs/yd³) Type C Fly Ash 101 88 113 109 $47.00/Ton(lbs/yd³) Sand (lbs/yd³) 1768 1721 1742 1671 $8.12/Ton 1 inch Rock 14661429 1446 1387 $9.36/Ton (lbs/yd³) Potable Water 288 263 288 266negligible (lbs/yd³) Daravair 0 1.4 0 1.4 $3.75/Gal (fl. oz./cwt) % Air2.5 5.6 2.5 5.2 $5.65/Gal Cost ($/yd³) $34.18 $31.38 $36.34 $35.09 —Weighted Avg. Cost $34.59 — ($/yd³) Cost Savings ($/yd³) $3.99 $5.16$8.16 $6.80 — Per Mix Design Weighted Avg. $6.66 — Plant Cost Savings($/yd³)

Each improved mix design of Examples 9-12 is able to take the place ofthree pre-existing standard mix designs of similar type because itsatisfies the criteria of all three mix designs while also havingreduced cost. The reduced number of mix designs is an additional costsavings as it simplifies the overall manufacturing process.

The absolute cost savings ranged from a low of $2.04 per yard (Example 9relative to Comparative Example 9a) to a high of $10.96 per yard(Example 12 relative to Comparative Example 12c). The weighted averagecost of the pre-existing mix designs of Comparative Examples 9a-12c,based on the percentage of each mix design sold by the manufacturingplant, is $41.24 per yard (as of Oct. 27, 2005). The weighted averagecost to manufacture concrete using the four optimized mix designs basedon existing sales percentages for the 12 pre-existing mix designs of themanufacturer would be $34.59 per yard at the same materials cost percomponent. The average overall cost savings for the manufacturing plantwould therefore be $6.66 per yard, assuming the manufacturer were toreplace the 12 pre-existing mix designs of Comparative Examples 9a-12cwith the optimized mix designs of Examples 9-12 and continue tomanufacture the same distribution of concrete as before.

Examples 13-16

Examples 13-16 illustrate four optimized concrete mix designs that wereprepared using the improved DOC process described herein. The four mixdesigns of Examples 13-16 can replace twelve pre-existing standardconcrete mix designs of an existing concrete manufacturing plant, whichutilized the same 12 mix designs as in Comparative Examples 1a-4c butmanufactured concrete using a different set of raw materials. Each mixdesign of Examples 13-16 corresponds to a group of three pre-existingmix designs of similar type that guarantee a minimum compressivestrength, at a specified slump, and percentage of entrained air whendelivered to the customer. The pre-existing mix designs of the concretemanufacturing plant, their components, cost (revised Oct. 27, 2005), andapparent design K factors, will be presented in four groups of threeconcrete mix designs, each group having similar properties orcharacteristics.

Comparative Examples 13a-13c

The three mix designs of Comparative Examples 13a-13c have a designstrength of 3000 psi, a slump of 4 inches, and minimal entrained air(1.5%). Comparative Example 13a 13b 13c Cost (US$) Compressive Strength3000 3000 3000 — (psi) Slump (inch) 4 4 4 — Type 1 Cement 370 470 423$104/Ton (lbs/yd³) Type C Fly Ash 100 0 0 $47.00/Ton (lbs/yd³) Sand(lbs/yd³) 1570 1470 1660 $8.12/Ton Pea Gravel (lbs/yd³) 1700 1700 1714$9.36/Ton Potable Water (lbs/yd³) 280 280 265 Negligible Daravair (airentrain.) 0 0 0 $3.75/Gal (fl. oz./cwt) Daracem (water red.) 0 0 14.8$5.65/Gal (fl. oz./cwt) % Air 1.5 1.5 1.5 — Apparent Design K 234 191207 — Factor Cost ($/yd³) $36.14 $38.57 $39.75 — Sales Distribution (%)19.57 80.43 0 — Within Group Weighted Average $38.10 — Cost ($/yd³)Total Sales (%) of 1.08 — Concrete Plant

Comparative Examples 14a-14c

The three mix designs of Comparative Examples 14a-14c have a designstrength of 3000 psi, a slump of 4 inches, and substantial entrained air(5%). Comparative Example 14a 14b 14c Cost (US$) Compressive Strength3000 3000 3000 — (psi) Slump (inch) 4 4 4 — Type 1 Cement 350 470 423$104/Ton (lbs/yd³) Type C Fly Ash 100 0 0 $47.00/Ton (lbs/yd³) Sand(lbs/yd³) 1510 1420 1560 $8.12/Ton Pea Gravel (lbs/yd³) 1750 1750 1740$9.36/Ton Potable Water (lbs/yd³) 250 260 240 Negligible Daravair (airentrain.) 4 5 4 $3.75/Gal (fl. oz./cwt) Daracem (water red.) 0 0 14.8$5.65/Gal (fl. oz./cwt) % Air 5 5 5 — Apparent Design K 237 189 199 —Factor Cost ($/yd³) $35.50 $39.29 $39.95 — Sales Distribution (%) 74.2325.77 0 — Within Group Weighted Average $36.47 — Cost ($/yd³) TotalSales (%) of 17.53 — Concrete Plant

Comparative Examples 15a-15c

The three mix designs of Comparative Examples 15a-15c have a designstrength of 4000 psi, a slump of 4 inches, and minimal entrained air(1.5%). Comparative Example 15a 15b 15c Cost (US$) Compressive Strength4000 4000 4000 — (psi) Slump (inch) 4 4 4 — Type 1 Cement 470 564 517$104/Ton (lbs/yd³) Type C Fly Ash 100 0 0 $47.00/Ton (lbs/yd³) Sand(lbs/yd³) 1530 1440 1530 $8.12/Ton Pea Gravel (lbs/yd³) 1746 1750 1750$9.36/Ton Potable Water (lbs/yd³) 280 285 280 Negligible Daravair (airentrain.) 0 0 0 $3.75/Gal (fl. oz./cwt) Daracem (water red.) 0 0 18.1$5.65/Gal (fl. oz./cwt) % Air 1.5 1.5 1.5 — Apparent Design K 232 206226 — Factor Cost ($/yd³) $41.39 $43.57 $45.63 — Sales Distribution (%)6.81 44.35 48.84 — Within Group Weighted Average $44.43 — Cost ($/yd³)Total Sales (%) of 12.81 — Concrete Plant

Comparative Examples 16a-16c

The three mix designs of Comparative Examples 16a-16c have a designstrength of 4000 psi, a slump of 4 inches, and substantial entrained air(5%). Comparative Example 16a 16b 16c Cost (US$) Compressive Strength4000 4000 4000 — (psi) Slump (inch) 4 4 4 — Type 1 Cement 470 564 517$104/Ton (lbs/yd³) Type C Fly Ash 100 0 0 $47.00/Ton (lbs/yd³) Sand(lbs/yd³) 1390 1340 1430 $8.12/Ton Pea Gravel (lbs/yd³) 1710 1750 1750$9.36/Ton Potable Water (lbs/yd³) 255 275 255 negligible Daravair (airentrain.) 4 5 4 $3.75/Gal (fl. oz./cwt) Daracem (water red.) 0 0 18.1$5.65/Gal (fl. oz./cwt) % Air 5 5 5 — Apparent Design K 224 212 218 —Factor Cost ($/yd³) $41.19 $43.98 $45.97 — Sales Distribution (%) 77.3122.69 0 — Within Group Weighted Average $41.82 — Cost ($/yd³) TotalSales (%) of 68.58 — Concrete Plant

The following optimized concrete mix designs according to Examples 13-16were made according to the improved DOC process and are intended toreplace the 12 mix designs of Comparative Examples 13a-16c. Eachoptimized mix design takes the place of three mix designs of similarattributes (e.g., the optimized mix design of Example 13 takes the placeof the pre-existing mix designs of Comparative Examples 13a-13c). Theoptimization procedure assumed a percent absorption for the sand and peagravel of 1.9% and 2.6%, respectively, and a percent moisture of 4.57%and 3.18%, respectively. Example 13 14 15 16 Cost (US$) Compressive 30003000 4000 4000 — Strength (psi) Slump (inch) 5 5 5 5 — Type 1 Cement 352305 403 373 $104/Ton (lbs/yd³) Type C Fly Ash 106 91 121 112 $47.00/Ton(lbs/yd³) Sand (lbs/yd³) 1734 1692 1690 1648 $8.12/Ton Pea Gravel(lbs/yd³) 1429 1394 1392 1358 $9.36/Ton Potable Water 288 277 310 277negligible (lbs/yd³) Daravair 0 1.4 0 1.4 $3.75/Gal (fl. oz./cwt) % Air2.4 5.8 2.6 5.8 $5.65/Gal Cost ($/yd³) $34.75 $31.74 $37.40 $35.45 —Weighted Avg. Cost $35.04 — ($/yd³) Cost Savings ($/yd³) $3.34 $4.73$7.03 $6.37 — Per Mix Design Weighted Avg. $6.14 — Plant Cost Savings($/yd³)

Each improved mix design of Examples 13-16 is able to take the place ofthree pre-existing standard mix designs of similar type because itsatisfies the criteria of all three mix designs while also havingreduced cost. The reduced number of mix designs is an additional costsavings as it simplifies the overall manufacturing process.

The absolute cost savings ranged from a low of $1.39 per yard (Example13 relative to Comparative Example 13a) to a high of $10.53 per yard(Example 16 relative to Comparative Example 16c). The weighted averagecost of the pre-existing mix designs of Comparative Examples 13a-16c,based on the percentage of each mix design sold by the manufacturingplant, is $41.18 per yard (as of Oct. 27, 2005). The weighted averagecost to manufacture concrete using the four optimized mix designs basedon existing sales percentages for the 12 pre-existing mix designs of themanufacturer would be $35.04 per yard at the same materials cost percomponent. The average overall cost savings for the manufacturing plantwould therefore be $6.14 per yard, assuming the manufacturer were toreplace the 12 pre-existing mix designs of Comparative Examples 13a-16cwith the optimized mix designs of Examples 13-16 and continue tomanufacture the same distribution of concrete as before.

Examples 17-20

Examples 17-20 illustrate four optimized concrete mix designs that wereprepared using the improved DOC process described herein. The four mixdesigns of Examples 17-20 can replace twelve pre-existing standardconcrete mix designs of an existing concrete manufacturing plant thatutilized the same 12 mix designs as in Comparative Examples 1a-4c butmanufactured concrete using a different set of raw materials. Each mixdesign of Examples 17-20 corresponds to a group of three pre-existingmix designs of similar type that guarantee a minimum compressivestrength, at a specified slump, and percentage of entrained air whendelivered to the customer. The pre-existing mix designs of the concretemanufacturing plant, their components, cost (revised Oct. 27, 2005), andapparent design K factors, will be presented in four groups of threeconcrete mix designs, each group having similar properties orcharacteristics.

Comparative Examples 17a-17c

The three mix designs of Comparative Examples 17a-17c have a designstrength of 3000 psi, a slump of 4 inches, and minimal entrained air(1.5%). Comparative Example 17a 17b 17c Cost (US$) Compressive Strength3000 3000 3000 — (psi) Slump (inch) 4 4 4 — Type 1 Cement 370 470 423$104/Ton (lbs/yd³) Type C Fly Ash 100 0 0 $47.00/Ton (lbs/yd³) Sand(lbs/yd³) 1570 1470 1660 $10.80/Ton 1 inch Rock (lbs/yd³) 1700 1700 1714$6.25/Ton Potable Water (lbs/yd³) 280 280 265 Negligible Daravair (airentrain.) 0 0 0 $3.75/Gal (fl. oz./cwt) Daracem (water red.) 0 0 14.8$5.65/Gal (fl. oz./cwt) % Air 1.5 1.5 1.5 — Apparent Design K 234 191207 — Factor Cost ($/yd³) $35.61 $37.91 $39.35 — Sales Distribution (%)19.57 80.43 0 — Within Group Weighted Average $37.46 — Cost ($/yd³)Total Sales (%) of 1.08 — Concrete Plant

Comparative Examples 18a-18c

The three mix designs of Comparative Examples 18a-18c have a designstrength of 3000 psi, a slump of 4 inches, and substantial entrained air(5%). Comparative Example 18a 18b 18c Cost (US$) Compressive Strength3000 3000 3000 — (psi) Slump (inch) 4 4 4 — Type 1 Cement 350 470 423$104/Ton (lbs/yd³) Type C Fly Ash 100 0 0 $47.00/Ton (lbs/yd³) Sand(lbs/yd³) 1510 1420 1560 $10.80/Ton 1 inch Rock (lbs/yd³) 1750 1750 1740$6.25/Ton Potable Water (lbs/yd³) 250 260 240 Negligible Daravair (airentrain.) 4 5 4 $3.75/Gal (fl. oz./cwt) Daracem (water red.) 0 0 14.8$5.65/Gal (fl. oz./cwt) % Air 5 5 5 — Apparent Design K 237 189 199 —Factor Cost ($/yd³) $34.81 $38.47 $39.35 — Sales Distribution (%) 74.2325.77 0 — Within Group Weighted Average $35.75 — Cost ($/yd³) TotalSales (%) of 17.53 — Concrete Plant

Comparative Examples 19a-19c

The three mix designs of Comparative Examples 19a-19c have a designstrength of 4000 psi, a slump of 4 inches, and minimal entrained air(1.5%). Comparative Example 19a 19b 19c Cost (US$) Compressive Strength4000 4000 4000 — (psi) Slump (inch) 4 4 4 — Type 1 Cement 470 564 517$104/Ton (lbs/yd³) Type C Fly Ash 100 0 0 $47.00/Ton (lbs/yd³) Sand(lbs/yd³) 1530 1440 1530 $10.80/Ton 1 inch Rock (lbs/yd³) 1746 1750 1750$6.25/Ton Potable Water (lbs/yd³) 280 285 280 Negligible Daravair (airentrain.) 0 0 0 $3.75/Gal (fl. oz./cwt) Daracem (water red.) 0 0 18.1$5.65/Gal (fl. oz./cwt) % Air 1.5 1.5 1.5 — Apparent Design K 232 206226 — Factor Cost ($/yd³) $40.73 $42.78 $44.97 — Sales Distribution (%)6.81 44.35 48.84 — Within Group Weighted Average $43.71 — Cost ($/yd³)Total Sales (%) of 12.81 — Concrete Plant

Comparative Examples 20a-20c

The three mix designs of Comparative Examples 20a-20c have a designstrength of 4000 psi, a slump of 4 inches, and substantial entrained air(5%). Comparative Example 20a 20b 20c Cost (US$) Compressive Strength4000 4000 4000 — (psi) Slump (inch) 4 4 4 — Type 1 Cement 470 564 517$104/Ton (lbs/yd³) Type C Fly Ash 100 0 0 $47.00/Ton (lbs/yd³) Sand(lbs/yd³) 1390 1340 1430 $10.80/Ton 1 inch Rock (lbs/yd³) 1710 1750 1750$6.25/Ton Potable Water (lbs/yd³) 255 275 255 negligible Daravair (airentrain.) 4 5 4 $3.75/Gal (fl. oz./cwt) Daracem (water red.) 0 0 18.1$5.65/Gal (fl. oz./cwt) % Air 5 5 5 — Apparent Design K 224 212 218 —Factor Cost ($/yd³) $40.40 $43.06 $45.17 — Sales Distribution (%) 77.3122.69 0 — Within Group Weighted Average $41.00 — Cost ($/yd³) TotalSales (%) of 68.58 — Concrete Plant

The following optimized concrete mix designs according to Examples 17-20were made according to the improved DOC process and are intended toreplace the 12 mix designs of Comparative Examples 17a-20c. Eachoptimized mix design takes the place of three mix designs of similarattributes (e.g., the optimized mix design of Example 17 takes the placeof the pre-existing mix designs of Comparative Examples 17a-17c). Theoptimization procedure assumed a percent absorption for the sand androck of 1.9% and 3.2%, respectively, and a percent moisture of 4.57% and3.18%, respectively. Example 17 18 19 20 Cost (US$) Compressive 30003000 4000 4000 — Strength (psi) Slump (inch) 5 5 5 5 — Type 1 Cement 335302 374 366 $104/Ton (lbs/yd³) Type C Fly Ash 101 91 112 110 $47.00/Ton(lbs/yd³) Sand (lbs/yd³) 1762 1693 1740 1658 $10.80/Ton 1 inch Rock 14221366 1404 1337 $6.25/Ton (lbs/yd³) Potable Water 295 274 295 270negligible (lbs/yd³) Daravair 0 1.4 0 1.4 $3.75/Gal (fl. oz./cwt) % Air2.4 5.5 2.2 5.5 $5.65/Gal Cost ($/yd³) $34.01 $31.63 $36.12 $35.14 —Weighted Avg. Cost $34.64 — ($/yd³) Cost Savings ($/yd³) $3.45 $4.12$7.59 $5.86 — Per Mix Design Weighted Avg. $5.75 — Plant Cost Savings($/yd³)

Each improved mix design of Examples 17-20 is able to take the place ofthree pre-existing standard mix designs of similar type because itsatisfies the criteria of all three mix designs while also havingreduced cost. The reduced number of mix designs is an additional costsavings as it simplifies the overall manufacturing process.

The absolute cost savings ranged from a low of $1.60 per yard (Example17 relative to Comparative Example 17a) to a high of $10.03 per yard(Example 20 relative to Comparative Example 20c). The weighted averagecost of the pre-existing mix designs of Comparative Examples 17a-20c,based on the percentage of each mix design sold by the manufacturingplant, is $40.39 per yard (as of Oct. 27, 2005). The weighted averagecost to manufacture concrete using the four optimized mix designs basedon existing sales percentages for the 12 pre-existing mix designs of themanufacturer would be $34.64 per yard at the same materials cost percomponent. The average overall cost savings for the manufacturing plantwould therefore be $5.75 per yard, assuming the manufacturer were toreplace the 12 pre-existing mix designs of Comparative Examples 17a-20cwith the optimized mix designs of Examples 17-20 and continue tomanufacture the same distribution of concrete as before.

The next two examples are newly optimized mix designs for self-levelingconcrete. Self-leveling concrete manufactured according to the mixdesigns of Examples 21 and 22 is characterized as having sufficientlyhigh slump such that it can level out due to gravity alone withoutworking and also having sufficient cohesiveness such that it does notsignificantly segregate (i.e., separate into heavier and lightercomponents due to gravity).

Example 21

The follow mix design for a self leveling concrete composition wasdesigned using the improved DOC process disclosed herein. Suchcompositions are characterized as being air entrained and having greaterthan an 8-inch slump when in a wet condition prior to curing and aminimum compressive strength of 4000 psi after 7 days of curing. Allweights are SSD. Component Amount Cement 519 lbs/yd³ Fly Ash 130 lbs/yd³Sand 1857 lbs/yd³ Rock 1245 lbs/yd³ Water 261 lbs/yd³ Daravair 1.3fl.oz/cwt* P. NC534 11.6 fl.oz/cwt Glenium 3030 5.0 fl.oz/cwt*Note:Glenium added at plant for 4″ slump; Daravair adjusted at plant for min.5% air; accelerator added on-site followed immediately by adjustment ofslump on-site with additional Glenium 3030 if necessary.

Example 22

The follow mix design for a self leveling concrete composition wasdesigned using the improved DOC process disclosed herein. Suchcompositions are characterized as being air entrained and having greaterthan an 8-inch slump when in a wet condition prior to curing and aminimum compressive strength of 4000 psi after 7 days of curing. Allweights are SSD. Component Amount Cement 366 lbs/yd³ Fly Ash 110 lbs/yd³Sand 1801 lbs/yd³ Rock 1219 lbs/yd³ Water 261 lbs/yd³ Daravair 1.3fl.oz/cwt* Rheomac VMA450 4.0 fl.oz/cwt Glenium 3030 2.0 fl.oz/cwt*

-   -   Note: Rheomac added at plant with batch water; Daravair adjusted        at plant for min. 5% air; on-site adjustment of slump with        Glenium 3030

The present invention may be embodied in other specific forms withoutdeparting from its spirit or essential characteristics. The describedembodiments are to be considered in all respects only as illustrativeand not restrictive. The scope of the invention is, therefore, indicatedby the appended claims rather than by the foregoing description. Allchanges which come within the meaning and range of equivalency of theclaims are to be embraced within their scope.

1. A method of determining whether an existing concrete compositionhaving a given design strength and given ratio of components isoverdesigned without having to (i) prepare a concrete test sample, (ii)allow it to harden, (iii) test its actual strength, and (iv) compare theactual strength of the test sample with the given design strength, themethod comprising: determining an apparent design K factor for theexisting concrete composition based on the given design strength of theconcrete composition and the given ratio of components within theconcrete composition; and comparing the apparent design K factor with amore optimal K factor that corresponds to the given design strength andwhich is selected from among a plurality of different K factors thatvary with varying concrete strength.
 2. A method as defined in claim 1,further comprising determining how much the existing concretecomposition is overdesigned by determining a deviation between theapparent design K factor of the existing concrete composition and themore optimal K factor.
 3. A method as defined in claim 1, furthercomprising identifying a ratio hydraulic cement, water and air for theexisting concrete composition, the apparent design K factor beingdetermined based on the ratio hydraulic cement, water and air.
 4. Amethod as defined in claim 1, further comprising using a computingsystem when determining the apparent design K factor.
 5. A method ofdetermining whether a concrete mix design used in manufacturing aconcrete composition having a given design strength and given ratio ofcomponents is overdesigned without having to (i) prepare a concrete testsample, (ii) allow it to harden, (iii) test its actual strength, and(iv) compare the actual strength of the test sample with the givendesign strength, the method comprising: determining an apparent design Kfactor for the concrete mix design based on the given design strength ofthe concrete composition and the given ratio of components within theconcrete composition; and comparing the apparent design K factor with amore optimal K factor that corresponds to the given design strength andwhich is selected from among a plurality of different K factors thatvary with varying concrete strength.
 6. A method as defined in claim 5,further comprising determining how much the concrete mix design isoverdesigned by determining a deviation between the apparent design Kfactor for the concrete mix design and the more optimal K factor.
 7. Amethod as defined in claim 5, further comprising identifying a ratiohydraulic cement, water and air within concrete manufactured using theconcrete mix design, the apparent design K factor being determined basedon the ratio hydraulic cement, water and air.
 8. A method as defined inclaim 5, further comprising using a computing system when determiningthe apparent design K factor.
 9. A method of determining whether anexisting concrete composition having a given design strength isoverdesigned without having to (i) prepare a concrete test sample, (ii)allow it to harden, (iii) test its actual strength, and (iv) compare theactual strength of the test sample with the given design strength, themethod comprising: selecting an optimal design K factor for an optimalconcrete composition in which actual strength approximates or equals thegiven design strength, wherein the optimal design K factor is selectedfrom among a plurality of different optimal K factors that vary withvarying concrete strength; determining an apparent design K factor forthe existing concrete composition based on the given design strength ofthe concrete composition and a given ratio of hydraulic cement, waterand air within a paste fraction of the concrete composition; andcomparing the apparent design K factor with the optimal K factor.
 10. Amethod as defined in claim 9, further comprising determining how muchthe concrete mix design is overdesigned by determining a deviationbetween the apparent design K factor of the existing concretecomposition and the optimal design K factor.
 11. A method as defined inclaim 9, further comprising using a computing system when determiningthe apparent design K factor of the existing concrete composition andcomparing the apparent design K factor with the optimal K factor.
 12. Amethod as defined in claim 9, further comprising redesigning theexisting concrete composition by means of an optimization procedure thatutilizes a revised design K factor that more closely correlates with theoptimal K factor for the given design strength than the apparent designK factor, wherein the optimization procedure yields a revised concretecomposition having an actual strength that more closely correlates withthe design strength compared to the existing concrete composition.
 13. Amethod as defined in claim 12, wherein the existing concrete compositionis redesigned using a computing system.
 14. A method as defined in claim9, further comprising: constructing an optimal K factor curve for agiven set of raw materials by identifying an optimal K factor pointrepresentative of a concrete strength value and then constructing anoptimal K factor curve that passes through that point and that isrepresentative of optimal K factors that vary with varying concretestrength; and selecting the optimal design K factor from the K factorcurve.
 15. A method as defined in claim 9, further comprisingconstructing a K factor curve for a concrete manufacturing plant bytesting actual strengths of a plurality of properly prepared concretecompositions of the manufacturing plant, determining a K factor for eachconcrete composition based on the actual strength and ratio of hydrauliccement, water and air in the composition, and plotting the actual Kfactors versus actual strength so as to construct the K factor curve.16. A method of determining whether a concrete mix design used inmanufacturing a concrete composition having a given design strength isoverdesigned without having to (i) prepare a concrete test sample, (ii)allow it to harden, (iii) test its actual strength, and (iv) compare theactual strength of the test sample with the given design strength, themethod comprising: selecting an optimal design K factor for an optimizedconcrete mix design in which actual strength approximates or equals thegiven design strength, wherein the optimal design K factor is selectedfrom among a plurality of different optimal K factors that vary withvarying concrete strength; determining an apparent design K factor forthe concrete mix design based on the given design strength of theconcrete composition and a given ratio of hydraulic cement, water andair within a paste fraction of the concrete composition; and comparingthe apparent design K factor with the optimal K factor.
 17. A method asdefined in claim 16, further comprising determining how much theconcrete mix design is overdesigned by determining a deviation betweenthe apparent design K factor of the concrete mix design and the optimaldesign K factor.
 18. A method as defined in claim 16, further comprisingusing a computing system when determining the apparent design K factorof the concrete mix design and comparing the apparent design K factorwith the optimal K factor.
 19. A method as defined in claim 16, furthercomprising redesigning the concrete mix design by means of acomputer-implemented optimization procedure that utilizes a reviseddesign K factor that more closely correlates with the optimal K factorfor the given design strength than the apparent design K factor, whereinthe optimization procedure yields a revised concrete mix design thatyields a concrete composition having an actual strength that moreclosely correlates with the design strength compared to the existingconcrete mix design.
 20. A method as defined in claim 19, furthercomprising: constructing a design K factor curve for a given set of rawmaterials used to manufacture concrete at a concrete manufacturing plantby identifying one or more design K factor points representative of oneor more concrete strength values and then constructing a design K factorcurve that passes through the one or more design K factor points andthat is representative of design K factors that vary with varyingconcrete strength; and selecting the revised design K factor from thedesign K factor curve.